the craving-practice leads to the origin of feeling

From SN 36.23:

Paṭipadā is placing at the same position of upādāna (clinging), so we can find the answer in the sutta that including clinging, craving, and feeling together, such as the four noble truth in Sutta. See Saṃ. Ma. DhammacakkappavattanaSutta:

"Now this, monks, is the noble truth of stress:1 Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, & despair are stressful; association with the unbeloved is stressful, separation from the loved is stressful, not getting what is wanted is stressful. In short, the five clinging-aggregates are stressful.
"And this, monks, is the noble truth of the origination of stress: the craving that makes for further becoming — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving for becoming, craving for non-becoming.

The feeling is an aggregate, and the craving origins clinging-aggregates, so the practicing of craving origin the feeling aggregate. See Sutta. Ma. U. Mahāpuṇṇamasuttaṃ:

"Monk, these are the five clinging-aggregates, i.e., form as a clinging-aggregate, feeling... perception... fabrications... consciousness as a clinging-aggregate."

Therefore, the last question in SN 36.23 is about the noble eightfold path of the four noble truth:

Q:What’s the origin of feeling? katamā nu kho, bhante, vedanā?
...
A: Feeling originates from contact. Phassasamudayā vedanāsamudayo.
...
Q: What’s the practice that leads to the origin of feeling? katamo vedanāsamudayo, katamā vedanāsamudayagāminī paṭipadā?
...
A: Craving is the practice that leads to the origin of feeling. Taṇhā vedanāsamudayagāminī paṭipadā.
...
Q: What’s the cessation of feeling? Katamo vedanānirodho?
...
A: When contact ceases, feeling ceases. Phassanirodhā vedanānirodho.
...
Q: What’s the practice that leads to the cessation of feeling? katamā vedanānirodhagāminī paṭipadā?
...
A: The practice that leads to the cessation of feelings is simply this
noble eightfold path, that is:
Ayameva ariyo aṭṭhaṅgiko maggo vedanānirodhagāminī paṭipadā,
seyyathidaṃ—
right view, right thought, right speech, right action, right
livelihood, right effort, right mindfulness, and right immersion.
sammādiṭṭhi … pe … sammāsamādhi.
...

The explanation of SN 35.23 Sabba Sutta in ṢaḷāyatanaVagga

0. History base knowledge about wrong and right view: See SarathW's Answer.
Then:

1. Why are these called "The All": the eye & forms, ear & sounds, nose & aromas, tongue & flavors, body & tactile sensations, intellect & ideas?
2. Why someone trying to explain "The All" as being something else would fail?
3. What does "it lies beyond range" mean?

The wrong view has the wrong condition(s). The right view has the right condition(s). The all right condition is the dependent origination, because the conditioner and the conditioned relate each other in balance, nothing left out of the cycle of the condition.
the dependent origination explains "Thus arises this whole mass of dukkha".
Each conditioner of the dependent origination causes the whole conditioned effect. For the example, ... the (Six-)Saḷāyatanas-conditioner causes the whole conditioned Six-Phassa; The Six-Phassa-conditioner cause the conditioned six-vedanā ...
So, if one, who questioned, explains the All, whole, into the dependent origination as the Buddha did, that one is able to explain the whole from the beginning to the end follow to the dependent origination such as the Buddha can explain every view in Sutta. Tī. Sī Brahmajālasuttaṃ.
But if one, who questioned, explains the All, whole, out of the dependent origination, that one would be unable to explain, and furthermore, would feel hard to answer (fail). Why? Because it is beyond that one's abilities, he exactly answers the wrong condition (fail), i.e. God condition the being.
SN KhandhaVagga and SN ṢaḷāyatanaVagga, such as SabbaSutta, come after SN Nidānavagga, the dependent origination because they are the whole elements which cycling in the dependent origination.

Buddhism's Existing Period Counting

The contexts about Buddhism's Existing Period Counting appear as 3 tenses in Aṭṭakathā:
1. The existing enlightenment of the current Buddha's follower (45BBE - about 5,000 BE):
Buddhism's existing period counting of current Buddha according to Vinaya.A. (samanta.3) Bhikkhunikkhandhakavaṇṇanā, An.A. (manoratha.1) Dutiyapamadadivaggavannana:
1st 1000 years after Gotama, Current Buddha, died:

Arahanta with Four Analytical Knowledges still occur=>

2nd 1000 years after GotamaSambuddha died:

Arahanta with Six Higher Knowledges still occur=>
Arahanta with Three Clear Knowledges still occur=>
Arahanta via Insight-only still occur=>>

3rd 1000 years after GotamaSambuddha died:

Anāgāmi with Four Analytical Knowledges still occur=>
Anāgāmi with Six Higher Knowledges still occur=>
Anāgāmi with Three Clear Knowledges still occur=>
Anāgāmi via Insight-only still occur=>>

4th 1000 years after GotamaSambuddha died:

Sakadāgāmi with Four Analytical Knowledges still occur=>
Sakadāgāmi with Six Higher Knowledges still occur=>
Sakadāgāmi with Three Clear Knowledges still occur=>
Sakadāgāmi via Insight-only still occur=>>

Final 1000 years after GotamaSambuddha died:

Sotāpanna with Four Analytical Knowledges still occur=>
Sotāpanna with Six Higher Knowledges still occur=>
Sotāpanna with Three Clear Knowledges still occur=>
Sotāpanna via Insight-only still occurs until the end of final 1000 years.

2. The previous KassapaBuddha (uncountable millions of years ago):
KassapaSamBuddha's, previous Buddha's, Buddhism existing period counting appear in Di.A. (sumangala.3) Sampasadaniyasuttavaṇṇanā; It using the past tense verbs). And Saṃ.A. (sārattha.2) Saddhammappaṭirūpakasuttavaṇṇanā, which connects to that Sampasadaniyasuttavaṇṇanā:
1st 1000 years after Kassapa, previous Buddha, died:

Arahanta with Four Analytical Knowledges still occur=>

2rd 1000 years after Kassapa, previous Buddha, died:

Arahanta with Six Higher Knowledges still occur=>

3th 1000 years after Kassapa, previous Buddha, died:

Arahanta with Three Clear Knowledges still occur=>

4th 1000 years after Kassapa, previous Buddha, died:

Arahanta via Insight-only still occur=>>

Final 1000 years after Kassapa, previous Buddha, died:

Pāṭimokkha memorizer still occurs until the end of final 1000 years.

3. The current Buddha's living time (45 - 0 BBE):
The sequence of existing enlightenment of the Buddha's followers just in current alive buddha's time, not died, appear in Saṃ.A. (sārattha.2) Saddhammappaṭirūpakasuttavaṇṇanā.It's explaining the Buddha's answer to KassapaThera's question in Sutta. Saṃ. Ni. Saddhammappaṭirūpakasutta:

"What is the cause, lord, what is the reason, why before there were fewer training rules and yet more monks established in final gnosis, whereas now there are more training rules and yet fewer monks established in final gnosis?"

At alive GotamaSamBuddha's time after he has enlightened, at the beginning Arahanta with Four Analytical Knowledges still occur. As time went by Arahanta with Six Higher Knowledges still occur Arahanta with Three Clear Knowledges still occur. As time went by Arahanta via Insight-only still occur. As time went by Anāgāmī still occur. As time went by Sakadāgāmi still occur. As time went by Sotāpanna still occur. As time went by Sīpavanta still occur.

---

A short term of all above Buddha's periods are up and down depending on the situation, but it tends to go down in long-term of every period. It's something like this:

Cr. wikipedia

The sequence concept of Theravāda Buddhism

The sequence concept of Theravāda Buddhism, start from sīla to paṭisambhidā, summarized from paṭisambhidāmagga, visuddhimagga, abhidhamma, atthhakathā, and all sāriputta's canons:
Paññā = understand the fact: causes&effects.
Paṭivedha = Paññā.
Ñāṇa = Expert Paññā.
Dassana = View, Understood, Diṭṭhi, Cakkhu.
SammāDiṭṭhi =SammāDassaṇa.
Ñātapariññā = Base of sammādassaṇa.
Tīraṇapariññā = Beginning sammādassaṇa practice.
Pahānapariññā = Advance sammādassaṇa practice.
Visuddhi = The base level which cleared from the extended enemy of the next level's enemy, so it is able to go to the next level.
Sīla = Arising physical & verbal behavior.
SīlaAdhiSikkhā = Physical & verbal behavior's training that supporting CittaVisuddhi.
SīlaVisuddhi = The CittaVisuddhi's base level which cleared from AvītikkamaKilesa, extending from CittaVisuddhi's enemy (PariyuṭṭhānaKilesa), so it is able to go to the next level, CittaVisuddhi.
AvītikkamaKilesa = Present life's arising physical & verbal unwholesome, extending from PariyuṭṭhānaKilesa.
PariyuṭṭhānaKilesa = Present life's arising mental unwholesome, extending from AnusayaKilesa.
AnusayaKilesa = Unwholesome behavior which ready to arise in the name "PariyuṭṭhānaKilesa". It arises as the name "PariyuṭṭhānaKilesa", but it stands as the name "AnusayaKilesa". It is similar to behavior because you can't find your behavior in any organ when you are not doing it, but you know your behavior still available to arise. The arising unwhole behavior is AvītikkamaKilesa/PariyuṭṭhānaKilesa.
Citta = Arising mind's behavior, Arising consciousness's behavior, arising Thought's behavior.
CittaAdhiSikkhā = Thought behavior's training that supporting DiṭṭhiVisuddhi.
CittaVisuddhi = The DiṭṭhiVisuddhi's base level which cleared from PariyuṭṭhānaKilesa, extending from DiṭṭhiVisuddhi's enemy (AttaAnuDiṭṭhiAnusayaKilesa), so it is able to go to the next level, DiṭṭhiVisuddhi.
SammāDassana = Right understood of conditioner and conditioned (four noble truth, dependent origination); diṭṭhivisuddhi + kaṇkhāvitaraṇavisuddhi; nāmarūpaparicchedañāṇa+paccayapariggahañāṇa; Ñātapariññā; Vipassanā Paññā; YathābūtaÑāṇaDassana.
four noble truth, dependent origination = conditioner aggregates and conditioned aggregates.
DiṭṭhiVisuddhi = The DiṭṭhiVisuddhi's base level which cleared from AttaAnuDiṭṭhiAnusayaKilesa, extending from KaṇkhāvitaraṇaVisuddhi's enemy (VisamahetukaDiṭṭhiAnusayaKilesa), so it is able to go to the next level, KaṇkhāvitaraṇaVisuddhi.
Attā (of the wrong view) = The misunderstood concept of conditioner aggregates and conditioned aggregates. This misunderstood concept make ordinary people think "there are some controllable aggregates left to be nihilistic or eternal". But the truth is "there are no any controllable aggregates to be nihilistic or eternal. There are only uncontrollable conditioner aggregates and uncontrollable conditioned aggregates".
AttaAnuDiṭṭhi = The misunderstood behavior about aggregates whether "some/whole aggregates are Attā".
KaṅkhāvitaraṇaVisuddhi = The MaggāmaggaÑāṇaDassanaVisuddhi's base level which cleared from VisamahetukaDiṭṭhiAnusayaKilesa, extending from MaggāmaggaÑāṇaDassanaVisuddhi's enemy (VipassanāUpakKilesa), so it is able to go to the next level, MaggāmaggaÑāṇaDassanaVisuddhi.
Vipassanā = SammāDassaṇa; VipassanāPaññā; Vipassanā; Ñātapariññā; Pajānāti.
Anupassnā = ÑāṇaDassaṇa; VipassanāÑāṇa; Vipassanā Bhāvanā; Vipassanā Meditation; Tīraṇapariññā + Pahānapariññā; Anupassati.
MaggāmaggaÑāṇaDassanaVisuddhi = SammāDassaṇa at cleared ñāṇa level from the extending enemy (the ignorant about the right or wrong practice [maggāmagga;paṭipadā]) of the next level's enemy (the ignorant about the four noble truth), so it is able to go to the next level, to practice watching three characteristics without confusing of the right or wrong practice; BapavaUdayabbayañāṇa.
PaṭipadāÑāṇaDassanaVisuddhi = above ÑāṇaDassana at cleared ñāṇa level from the extending enemy (the ignorant about the four noble truth) of the next level enemy (the ignorant about the four noble truth), so it is able to go to the next level, to stop the ignorant about the four noble truth forever by the complete&perfect watching three characteristics; From Bhaṅgañāṇa to Anulomañāṇa.
ÑāṇaDassanaVisuddhi = above ÑāṇaDassana at cleared ñāṇa level(enlightenment) from the extending enemy (fetters; saṇyojana) of the next level enemy (rebirth; becoming; bhava; paṭisandhiviññāṇa), so it is able to go to the next level, to stop the rebirth as many as the level of the enlightenment.
Paṭisambhidā = ÑāṇaDassanaVisuddhi according to Abhi. Vibhaṅgo ñāṇavatthuvibhaṅga, Sutta. Khu. Paṭisambhidāmaggo mahāvaggo ñāṇakathā mātikā, Paṭisambhidāmaggo's atthakathā, Visuddhimagga Khandhaniddeso. All ariya must enlighten Paṭisambhidā of own meditation. They can analysis everything about own meditation (super mundane jhāna), but they maybe don't know about mundane jhāna, Abhiññā, and the other practitioners' meditation. They enlightened Paṭisambhidā of own meditation only, they may be not the Paṭisambhidappatto.
Tevijjo = Ariya who is an expert, vasī, of jhāna. That expertise increases the power of ÑāṇaDassana to be greater, to be able to recall many past lives and to be able to recall many deaths&rebirths more than the practitioner who is no an expert of jhāna. Normally, the only vipassanā practitioner can recall about 1-2 past lives, but the expert of jhāna can recall more than that. The expert of jhāna spend the lesser time to recall the past lives at the same number of life.
Abhiññā = Special practice of an expert, vasī, of jhāna. Two Abhiññā, Pubbenivāsānussatiñāṇa and Cutūpapatañāṇa, have the similar practice as ÑāṇaDassaṇa, so the expert of jhāna can enlighten as a Tevijjo easier.
Chaḷabhiñño = Ariya who is an expert, vasī, of every Abhiññā.
Paṭisambhidappatto = Chaḷabhiñño who is an expert of own and the others' Paṭisambhidā.
For the example question:

if I become a stream-enterer I will automatically have four analytical knowledge right? Will I also have three clear knowledge and six higher knowledge?

if you become a stream-enterer without being an expert of jhāna&abhiñña&paṭisambhidā, you are a stream-enterer who automatically have only four analytical knowledge right of your meditation. You are only a Sukkhavipassako, but you are not Paṭisambhidappatto, Chaḷabhiñño, Tevijjo.
For the conclusion:

In AN 4.171, what is “reincarnation where the intention of others is effective”?

Per commentary, this passage refers to "devas corrupted by the mind" (Manopadosika-deva), living in the world of the Four Great Kings. When they get angry with one another their mutual anger leads to their mutual deaths.
Here are descriptions of Manopadosika-deva from different sources:
Buddhist Dictionary. Manual of Buddhist Terms & Doctrines (4th Edition) by Ven. Nyanatiloka:

Manopadosika-deva: ‘the celestial beings corruptible by temper’, are a class of devas (q.v.) of the sensuous sphere. “They spend their time in becoming annoyed with one another, and getting into a temper, and thus by being bodily and mentally exhausted, they pass from that world” (D. 1; 24).

The "Dictionary of Pali Proper Names" by G. P. Malalasekera:

A class of devas living in the Cātummahārājika world (DA.i.114; AA.ii.544; MNid.108). They burn continually with envy one against another (Buddhaghosa relates a story illustrating this in DA.i.114) and their hearts become ill disposed and debauched. Their bodies thus become feeble and their minds imbecile, and, as a consequence, they fall from their state (D.i.20; iii.32). The Manopadosikā were among those present at the preaching of the Mahāsamaya Sutta (D.ii.260). They are so called because their minds are debauched by envy (dosassa anudahanatāya) (VibhA.498).

Brahmajāla Sutta (DN 1) translated from the Pali by Bhikkhu Bodhi:

There are, bhikkhus, certain gods called 'corrupted by mind.' These gods contemplate one another with excessive envy. As a consequence their minds becomes corrupted by anger towards one another. When their minds are corrupted by anger, their bodies and minds become exhausted and consequently, they pass away from that plane.

Brahmajāla Sutta (DN 1) translated by Bhikkhu Sujato:

There are gods named ‘malevolent’. They spend too much time gazing at each other, so they grow angry with each other, and their bodies and minds get tired. They pass away from that group of gods.

So, one deva's hatred towards another deva provokes hatred in that deva towards the first, causing a vicious circle, and this very hatred exhausts their spirits until they fall from their godly state.
One deva's hatred is not his own deliberate intention but is merely a reaction to another deva's hatred. Therefore the deva falls from his state and comes to a different state through an "intention of other".
It's interesting how the vicious circle of judgement starts not through one of the devas performing some unwelcomed act to another, but rather through both spending too much time wondering about the other's attitude to oneself.
I suppose this basically means that not all karma is strictly personal. While in the simplest cases sentient beings inherit their own karma, there are cases when they create (bad) karma for one another, and there are cases when a karmic pattern emerges spontaneously from a background of ignorance - not through anyone's fault.
On a side note, per my (Russian) dictionary, attabhāvapaṭilābhe is not "reincarnation" but "a state of personal existence".
by Andrei Volkov @https://buddhism.stackexchange.com/a/30153/10100.

---------------------

I agree with Andrei Volkov explanation, which follows to it's atthakathā. However, for the perfect understood by sutta, not only atthakathā, I write this answer.

1. There is a reincarnation where one’s own intention is effective, not that of others. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe attasañcetanā kamati, no parasañcetanā.

By atthakathā, above text refers to DN Brahmajālasuttaṃ:

7. ‘And what is the second?

‘There are, brethren, certain gods called the “Debauched by Pleasure” [155]. ‘For ages they pass their time in the pursuit of the laughter and sport of sensual lusts. In consequence thereof their self-possession is corrupted, and through the loss of their self-control they fall from that state [156].

8. ‘Now it might well be, brethren, that some being, on his falling from that state, should come hither. And having come hither he should, as in the last case, become a recluse, and acquire the power of recollecting his last birth, but only his last one.
9. ‘And he would say to himself: “Those gods who are not debauched by pleasure are stedfast, immutable, eternal, of a nature that knows no change, and they will remain so forever and ever. [20] But we-who fell from that state, having lost our self-control through being debauched by pleasure-we have come hither as being impermanent, mutable, limited in duration of life.”

By atthakathā, above text refers to MN kandarakasuttaṃ:

2. There is a reincarnation where the intention of others is effective, not one’s own. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe parasañcetanā kamati, no attasañcetanā.

Bhikkhus, which person torments others yoked to it? Bhikkhus, here a certain person is a killer of pigs, goats, birds, a hunter of wild animals, a fisherman, a robber, a highway robber, one who keeps a prison, or engaged in any other vicious activity. This person torments others yoked to tormenting others.

3. There is a reincarnation where both one’s own and others’ intentions are effective. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe attasañcetanā ca kamati parasañcetanā ca.

By atthakathā, above text refers to DN Brahmajālasuttaṃ:

10. ‘And what is the third?

‘There are, brethren, certain gods called "the Debauched in Mind [157].” They burn continually with envy [158] one against another, and being thus irritated, their hearts become ill-disposed towards each other, and being thus debauched, their bodies become feeble, and their minds imbecile. And those gods fall from that state.

11. ‘Now it might well be, brethren, that some [\q 034/] being, on his falling from that state, should come hither; and having become a recluse should ‘as in the other cases, acquire the power of recollecting his last birth, but only his last one.
12. ‘And lie would say to himself: “Those gods who are not debauched in mind do not continually burn with envy against each other, so their hearts do not become evil disposed one towards another, nor their bodies feeble and their minds imbecile. Therefore they fall not from that state; they are stedfast, immutable, eternal, of a nature that knows no change, and they will remain so forever and ever. [21] But we were corrupted in mind, being constantly excited by envy against one another. And being thus envious and corrupt our bodies became feeble, and our minds imbecile, and we fell from that state, and have come hither as Being impermanent, mutable, limited in duration of life.”

‘This, brethren, is the third case.

4. There is a reincarnation where neither one’s own nor others’ intentions are effective. Atthi, bhikkhave, attabhāvapaṭilābho, yasmiṃ attabhāvapaṭilābhe nevattasañcetanā kamati, no parasañcetanā.

By atthakathā, above text refers to DN Dānamahapphalasutta:

"Having given this gift seeking his own profit — with a mind attached [to the reward], seeking to store up for himself, [with the thought], 'I'll enjoy this after death' — on the break-up of the body, after death, he reappears in the company of the Devas of the Four Great Kings. Then, having exhausted that action, that power, that status, that sovereignty, he is a returner, coming back to this world.
"Having given this gift with the thought, 'Giving is good,' on the break-up of the body, after death, he reappears in the company of the Devas of the Thirty-three. Then, having exhausted that action, that power, that status, that sovereignty, he is a returner, coming back to this world.
...

Why I have to link? Theravāda tradition never allow to explain tipitaka without reference, linking. It's weird and not professional. If buddhaghosa wrote something without the reference, he wouldn't be allowed to translate atthakathā back to pāli. So, the link, which I have given, show tipitaka memorizer's thought.

Is suffering dependent on aging & death? If so, how is suffering experienced before & after death?

If death must occur for sorrow, lamentation, pain, distress & despair to come into play; what is the cause for people having sorrow, grief & despair before death, i.e., in the present moment?

If death must occur for sorrow, lamentation, pain, distress & despair to come into play; is sorrow, grief & despair only experienced after death?

Aging & death must come together to show "if you born without unstable, it's ok. But actually, your life is unstable because it's going to be aging & death, it's not ok. Because while you are living, birth+aging+death, you are going to have sorrow, lamentation, pain, distress & despair to come into play aging & death."

Pali context only shows birth causes "aging & death, sorrow, lamentation, pain, distress & despair to come into play". Nothing in pāli context shows aging & death cause "sorrow, lamentation, pain, distress & despair to come into play".

jātipaccayā jarāmaraṇaṃ sokaparidevadukkhadomanassupāyāsā sambhavanti.

So, your both questions are misunderstood pali context. There is nothing in pali context shows "death must occur for sorrow, lamentation, pain, distress & despair to come into play". Pāli only shows birth causes "aging & death, sorrow, lamentation, pain, distress & despair to come into play".

In the other hand by pāli context, the sequence of paṭiccasamuppāda is "birth >> aging&death, sorrow, lamentation, pain, distress & despair to come into play". It is not "birth >> aging >> death >> sorrow, lamentation, pain, distress & despair to come into play".

What does “sandhāvitvā saṃsaritvā” mean in AN 9.12?

1. What does "sattakkhattuparama" mean literally and non-literally?

sattakkhattuparama = not more than seven times.

Why did he include rebirth into his translation?

Because of the context below which come before "sattakkhattuparama" and being on the same topic:

There are these nine people who, dying with something left over, are exempt from hell, the animal realm, and the ghost realm. They’re exempt from places of loss, bad places, the underworld.

Navayime, sāriputta, puggalā saupādisesā kālaṃ kurumānā parimuttā nirayā parimuttā tiracchānayoniyā parimuttā pettivisayā parimuttā apāyaduggativinipātā.

...

With the ending of three fetters, and the weakening of greed, hate, and delusion, they’re a once-returner. They come back to this world once only, then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā rāgadosamohānaṃ tanuttā sakadāgāmī hoti, sakideva imaṃ lokaṃ āgantvā dukkhassantaṃ karoti.

...

With the ending of three fetters, they’re a one-seeder. They will be reborn just one time in a human existence, then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā ekabījī hoti, ekaṃyeva mānusakaṃ bhavaṃ nibbattetvā dukkhassantaṃ karoti.

...

With the ending of three fetters, they go family to family. They will transmigrate between two or three families and then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā kolaṅkolo hoti, dve vā tīṇi vā kulāni sandhāvitvā saṃsaritvā dukkhassantaṃ karoti.

Next question:

2. What is the meaning of the phrase "sandhāvitvā saṃsaritvā" in this quote? How does it relate to "sattakkhattuparama"?

saṃsaritvā is the synonym of sandhāvitvā. sandhāvitvā means transmigrate, transport, move next.

Translation: Person (puggalo) moves next(sandhāvitvā saṃsaritvā) not more than seven times (sattakkhattuparamaṃ) in deva [bhava] and human [bhava] (deve ca manusse ca) and then make the end of suffering (dukkhassantaṃ karoti).

3. Is the phrase "sandhāvitvā saṃsaritvā" used in other suttas, without being connected to "sattakkhattuparama"? What does it mean there? What is the context there?

Comepare with "sandhāvitvā saṃsaritvā" in MN Sandakasutta. It's context means "move to next life (rebirth)":

There are 1.4 million main wombs, and 6,000, and 600. There are 500 deeds, and five, and three. There are deeds and half-deeds. There are 62 paths, 62 sub-eons, six classes of rebirth, and eight stages in a person’s life. There are 4,900 Ājīvaka ascetics, 4,900 wanderers, and 4,900 naked ascetics. There are 2,000 faculties, 3,000 hells, and 36 realms of dust. There are seven percipient embryos, seven non-percipient embryos, and seven embryos without attachments. There are seven gods, seven humans, and seven goblins. There are seven lakes, seven winds, seven cliffs, and 700 cliffs. There are seven dreams and 700 dreams. There are 8.4 million great eons through which the foolish and the astute transmigrate before making an end of suffering.

Cuddasa kho panimāni yonipamukhasatasahassāni saṭṭhi ca satāni cha ca satāni pañca ca kammuno satāni pañca ca kammāni tīṇi ca kammāni, kamme ca aḍḍhakamme ca, dvaṭṭhipaṭipadā, dvaṭṭhantarakappā, chaḷābhijātiyo, aṭṭha purisabhūmiyo, ekūnapaññāsa ājīvakasate, ekūnapaññāsa paribbājakasate, ekūnapaññāsa nāgāvāsasate, vīse indriyasate, tiṃse nirayasate, chattiṃsa rajodhātuyo, satta saññīgabbhā, satta asaññīgabbhā, satta nigaṇṭhigabbhā, satta devā, satta mānusā, satta pesācā, satta sarā, satta pavuṭā, satta papātā, satta papātasatāni, satta supinā, satta supinasatāni, cullāsīti mahākappino satasahassāni, yāni bāle ca paṇḍite ca sandhāvitvā saṃsaritvā dukkhassantaṃ karissanti.

Next question:

4. Can I say that "sandhāvitvā saṃsaritvā" supports the interpretation of "sattakkhattuparama" as "seven lifetimes" or "seven rebirths"?

Actually, it is just a sign of many signs. Actually, the whole context of sutta supports the interpretation of "sattakkhattuparamo" as "person who has seven lifetimes left" or "person who has seven rebirths left". There are many signs to translate like that for the example:

With the ending of three fetters, they’re a one-seeder. They will be reborn just one time in a human existence, then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā ekabījī hoti, ekaṃyeva mānusakaṃ bhavaṃ nibbattetvā dukkhassantaṃ karoti.

1. Above quote's link is liking with many other suttas which force the translator to translate "ekaṃyeva bhavaṃ nibbattetvā" as "will be reborn just one time".
2. When the previous context translated "ekaṃyeva bhavaṃ nibbattetvā" as "will be reborn just one time", the next context have to translate follow it, too.

Person (puggalo) moves next(sandhāvitvā saṃsaritvā) not more than seven times (sattakkhattuparamaṃ) in deva [bhava] and human [bhava] (deve ca manusse ca) and then make the end of suffering (dukkhassantaṃ karoti).

I have to add 1 more question to complete this answer:

5. Why the buddha didn't use "nibbattetvā" with all person? Why the buddha used "sandhāvitvā saṃsaritvā" instead?

"Ekabījī (one-seeder)" will be reborn just one time (ekaṃyeva bhavaṃ nibbattetvā), but the next others will reborn multiple times. "sandhāvitvā saṃsaritvā" often use in multiple time rebirths.

Saupādisesasutta:

With the ending of three fetters, they’re a one-seeder. They will be reborn just one time in a human existence, then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā ekabījī hoti, ekaṃyeva mānusakaṃ bhavaṃ nibbattetvā dukkhassantaṃ karoti.

...

With the ending of three fetters, they go family to family. They will transmigrate between two or three families and then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā kolaṅkolo hoti, dve vā tīṇi vā kulāni sandhāvitvā saṃsaritvā dukkhassantaṃ karoti.

...

With the ending of three fetters, they have at most seven rebirths. They will transmigrate at most seven times among devas and humans and then make an end of suffering.

So tiṇṇaṃ saṃyojanānaṃ parikkhayā sattakkhattuparamo hoti, sattakkhattuparamaṃ deve ca manusse ca sandhāvitvā saṃsaritvā dukkhassantaṃ karoti.

MN Sandakasutta:

There are 1.4 million main wombs, and 6,000, and 600. There are 500 deeds, and five, and three. There are deeds and half-deeds. There are 62 paths, 62 sub-eons, six classes of rebirth, and eight stages in a person’s life. There are 4,900 Ājīvaka ascetics, 4,900 wanderers, and 4,900 naked ascetics. There are 2,000 faculties, 3,000 hells, and 36 realms of dust. There are seven percipient embryos, seven non-percipient embryos, and seven embryos without attachments. There are seven gods, seven humans, and seven goblins. There are seven lakes, seven winds, seven cliffs, and 700 cliffs. There are seven dreams and 700 dreams. There are 8.4 million great eons through which the foolish and the astute transmigrate before making an end of suffering.

Cuddasa kho panimāni yonipamukhasatasahassāni saṭṭhi ca satāni cha ca satāni pañca ca kammuno satāni pañca ca kammāni tīṇi ca kammāni, kamme ca aḍḍhakamme ca, dvaṭṭhipaṭipadā, dvaṭṭhantarakappā, chaḷābhijātiyo, aṭṭha purisabhūmiyo, ekūnapaññāsa ājīvakasate, ekūnapaññāsa paribbājakasate, ekūnapaññāsa nāgāvāsasate, vīse indriyasate, tiṃse nirayasate, chattiṃsa rajodhātuyo, satta saññīgabbhā, satta asaññīgabbhā, satta nigaṇṭhigabbhā, satta devā, satta mānusā, satta pesācā, satta sarā, satta pavuṭā, satta papātā, satta papātasatāni, satta supinā, satta supinasatāni, cullāsīti mahākappino satasahassāni, yāni bāle ca paṇḍite ca sandhāvitvā saṃsaritvā dukkhassantaṃ karissanti.

Buddhist objective is nibbāna, the safest, so the reader need to learn it hard step by step

Buddhist objective is nibbāna, the safest.
It's like the science's, engineering's or computer programming's rule, we can't misunderstand at any level of the process. It's buggy, risk and unsafe.
Therefore, it's very hard to understand Tipitaka and Atthakatha as alike as science's, engineering's or computer programming's rule.
So, if you point your expectation in Buddhism only at the easy part, you will miss the safest part, which elaborated multi aspects of reasons. That missing is buggy, risk and unsafe.
So, concrete exposition of Buddhism is the conclusion like:

1. Vinaya is in VN Parivāra by upāli, the vinaya secretary of buddha.
2. Sutta is in KN Paṭisambhidāmagga by sāriputta, the stand-in teacher of buddha in MN Mahāgosiṅgasālasutta (or alternative in translated Visuddhimagga but if you bias of the supernatural, it's not your choice).

Both above require these to understand:

1. Pāli skill from Kaccāyana.
2. Tipitaka analysis skill from Netti.
3. The discipline of everything from abhidhamma by sāriputta, the stand-in teacher of buddha in MN Mahāgosiṅgasālasutta. Or, saṅgaha by anuruddha, past laṅkā's pontiff.

But if you want to start in Buddhism, you need:

1. Qualified teacher to teach you step by step.
2. Easy sutta to recite and do follow, such as Maṅgalasutta (and all Khuddakapātha), Siṅgālakasutta, and dhammapatha.

The Pali word 'saṅkhārā' in Dependent Origination plural because it is the crossroad.

Dependent origination is the cycle of the happening event. Each event has only one decision. There are 2 saṅkhāra for each decision: wholesome and unwholesome. Wholesome saṅkhāra gives good resultants. Unwholesome saṅkhāra gives bad resultants. So, viññāna to vedanā which are the resultants of saṅkhāra must be singular, because it's just the resultants of one decision. Jāti and jarāmaraṇaṃ are same. Wholesome karmma-bhavo gives good resultants. Unwholesome karmma-bhavo gives bad resultants. So, jāti and jarāmaraṇaṃ must be singular because of the same reason.

Above explanation explained clearly in abhidhamma vibhaṅga paccayākāravibhaṅga and it's atthakathā. It separates each event to singular as "saṅkhāro". That's why no direct explaination in any atthakathā, included path of purification. However, it's used widely in difference context such as in VN.A. Introduction.

And this is the example of what I wrote "it's used widely":

Kusalattika: kusalā dhammā, akusalā dhammā, abyākatā dhammā.

The "wholesome" triad: wholesome phenomena, unwholesome phenomena, not both phenomena

The Path of Purification detailedly exposited the dependent origination follow to 'the "wholesome" triad':

jarāmaraṇaṃ = not both phenomena

jati = not both phenomena

bhavo = not both phenomena

upādānaṃ = unwholesome phenomena

taṇhā = unwholesome phenomena

vedanā = not both phenomena

phasso = not both phenomena

saḷāyatanaṃ = not both phenomena

nāmarūpaṃ = not both phenomena

viññāṇaṃ = not both phenomena

saṅkhārā = 1. wholesome phenomena, 2. unwholesome phenomena

avijjā = unwholesome phenomena

You can see whether saṅkhārā are separated into 2 events.

Above quote is my own conclusion. To read it, the reader needs to understand in advance of chapter XIV, XV, XVI, XVII, and some part of chapter I, III. Also, it requires Abhidhamma knowledge in advance, as well.

Path of Purification, CH. XVII, THE SOIL OF UNDERSTANDING—CONCLUSION, DEPENDENT ORIGINATION, III. Detailed Exposition page 547-608.

Did the Buddha ever define what he meant by “self”?

Anattalakkhaṇasutta is a short sutta for "self" explanation. 

Brahmajālasutta is a long sutta. 

All abhidhamma, especially paṭṭhāna, are "non self" explanation. This is the longest explanation. 

If you can't understand "self" by all of these sutta, it means your pali skill is lacking.

There are only two realities: saṅkhāra and asaṅkhāra; All others are paññatti

There are only two realities: saṅkhāra (dependent origination such as aggregate) and asaṅkhāra (no dependent origination such as nibbāna). All others are paññatti (concept;imagine;not reality) because saṅgkhāra must have tree sub-characteristics and asaṅkhāra must have not tree sub-characteristics. But paññatti has nothing, it can't arise like saṅkhāra and can't cease saṅkhāra like nibbāna.
By VN Parivāra of upāli-etadagga:

Aniccā sabbe saṅkhārā, dukkhānattā ca saṅkhatā; Nibbānañceva paññatti, anattā iti nicchayā.
Saṅkhāra, which means saṅkhata(effect-saṅkhāra)*, is anicca&dukkha&anattā; But only nibbāna&paññatti which are explained as only anattā.
(*Saṅkhāra, which means cause-saṅkhāra, use in more fixed meaning word, such as saṅkhāra-khandha, saṅkhāra-paṭiccasamuppāda. You can notice it in each context, because it is already appear clearly.)

And by KN Paṭisambhidāmagga of sāriputta-mahāsāvaka:

sabbe saṅkhārā aniccā sabbe saṅkhārā dukkhā sabbe dhammā anattāti
All saṅkhāra are anicca, all saṅkhāra are dukkha, and all dhammā are anattā.

There is no saṅkhāra which is not aggregates (Khandhavinimuttako hi saṅkhāro nāma natthi.)
Below, the second group is the conclusion of the first group, Sutta. Ma. Mū. Cūḷasaccakasuttaṃ:

"Aggivessana, 2 the Blessed One disciplines his disciples in this way; this part of the Blessed One's instruction is generally presented to his disciples: ('Form is inconstant. Feeling is inconstant. Perception is inconstant. Fabrications are inconstant. Consciousness is inconstant.) Form is not-self. Feeling is not-self. Perception is not-self. Fabrications are not-self. Consciousness is not-self. (All fabrications are inconstant.) All phenomena are not-self.' This, Aggivessana, is the way in which the Blessed One disciplines his disciples; this part of the Blessed One's instruction is generally presented to his disciples."

However, "All phenomena are not-self" in above context include more than "Form is inconstant", because it include more two, nibbāna and paññatti, as I have described above.
Abhidhamma and atthakathā have this same explanation as well.

Jhāna meditation defination

I am so sorry for the long answer. It's required all of this knowledge to understand the meditation's idea.

What is jhāna?

Jhāna (concentration meditation) is the meditation method to cease the desire (chanda-rāga) of the world (loka) by changing mind's attention to the opposite object of the world.

What is the world?

Living being (satta) is the world (loka), 5 clinging-aggregates (upādāna-khandha[1][2]).

Loka means breakable thing. And what we can notice 3 characteristics must be break, breakable. What is unstable (anicca), stressful (dukkha), and non-self (anattā) is what we can notice it's instability-characteristic (anicca-lakkhaṇa), e.g. it's arising and vanishing, stress-characteristic, e.g. it's stressing to arise and to vanish in every millisecond, and uncontrollable characteristic, e.g. it's variant variables.

Each aggregate has 3 characteristics, so every aggregate (pañca-khandha) is breakable, and it is called Loka. There are 2 kinds of breakable aggregates, lokiya (with clinging) and lokuttara (no clinging). However the practitioner should comprehend only clinging aggregates (upādāna-khandha) to meditate insight meditation, Buddha called clinging aggregates (upādāna-khandha), in first noble truth, not only aggregates (khandha).

The genius people can notice 3 characteristics of every living being, so they try to cease all possible cases of living beings' rebirth by the meditation.

There are many method of the meditation of those genius people which doing the difference methods and each method causes the difference results, some is not able to pause any world, some can pause 5 string world (kāma loka), some can pause form concept world (rūpa loka), some can cease all worlds (kāma loka/rūpa loka/arūpa loka).

How many kinds of jhāna?

There are 3 kinds of jhāna:

1. Form jhāna (rūpa jhāna) - meditation of changing mind's attention form five strings world (kāma-loka) to form's concept world (rūpa-paññatti-loka) to disable 5 sense attachments arising (kāmachandarāga). This meditation's step, 1st-4th jhāna, pause attachment of five strings and mental factors which can drop the quality of concentration down to five strings world. The attained people are going to reborn in the world without five string attachment, but it still has forms, such as eyes to watch the form to meditate rūpa-jhāna.
2. Formless jhāna (arūpa jhāna) - meditation of changing mind's attention form form's concept world to formless world (arūpa-loka) to disable all form arising, which make rūpa jhāna&world still nearby five strings attachment. This meditation change the object to detach from mind and mental factors (arūpa-loka) as much as they can. However, it's useless, the number of mental factors still be the same, 30 factors, from the 1st formless jhāna to the 4th formless jhāna. The attained people are going to reborn in the world without form, but it still have mind and mental factors (nāma-khandha).
3. Three characteristic jhāna (lakkhaṇa-jhāna) - vipassanā; insight meditation. Meditation of changing mind's attention form all worlds to nibbāna (cessation of world). The attained magga people do not reborn any more in maximum 7 rebirths.

Jhāna bases vipassanā, especially for the practitioner who attach five strings strongly (taṇhā-carita).

How to disable 5 sense attachment?

Keeping the sixth sense mind on concept object (paññatti;paṭibhāga-nimitta) by practice to change the the sixth sense memory of the five strings (kāmaguṇa) to concept object (paññatti;paṭibhāga-nimitta) then meditate that practice to go on for a long period, a hour or a day.

How to disable all form arising?

Keeping the sixth sense mind on the object which has no any relation with form (arūpa) by practice to change the the sixth sense memory of form concept (rūpa-paññatti;paṭibhāga-nimitta) to formless object (arūpa) then meditate that practice to go on for a long period, a hour or a day.

What is the problem?

The jhāna practitioner still keep the self attachment of their meditation mind&mind factors as "it's mine. It's me, not the other. It's myself, so I can control it". This is the reason why we need Buddha.

---

See Ma.Mu. Cūḷasīhanādasutta, Mahādukkhakkhandhasutta, the path of purification in pathavīkasiṇa chapter and aruppā chapter, and this article.

What is the meaning behind saṅghānussati chant?

For the meaning of saṅghānussati in advance, see Part II—Concentration (Samádhi) CH. VII SIX RECOLLECTIONS Recollection of the Saṅgha page 215.

We should be used with the tree refuges according to Sutta. Ma. U. Sevitabbāsevitabbasuttaṃ:

It was said, "Sāriputta, I say, persons are also twofold those that should be used and not used" On account of what was it said by the Blessed One? Venerable sir, when using certain persons demerit increases and merit decreases, such persons should not be used, when using certain persons demerit decreases and merit increases, such persons should be used. It was said, "Sāriputta, persons too are twofold, those that should be used and not used. " It was said on account of this.

Why? Sutta. Khu. Jā.(1) Vīsatinipātajātakaṃ Sattigumbajātakaṃ:

“To whomsoever, good or bad, a man shall honour pay, Vicious or virtuous, that man holds him beneath his sway.

“Like as the comrade one admires, like as the chosen friend, Such will become the man who keeps beside him, in the end.

“Friendship makes like, and touch by touch infects, you’ll find it true: Poison the arrow, and ere long the quiver’s poisoned too.

“The wise eschews bad company, for fear of staining touch: Wrap rotten fish in grass, you’ll find the grass stinks just as much. And they who keep fool’s company themselves will soon be such.

“Sweet frankincense wrap in a leaf, the leaf will smell as sweet. So they themselves will soon grow wise, that sit at wise men’s feet.

“By this similitude the wise should his own profit know, Let him eschew bad company and with the righteous go: Heaven waits the righteous, but the bad are doomed to hell below.”

Shyness is Coward; prompted.

Shyness is Coward; prompted.
In abhidhamma, minds and mental factor of sasaṅkhārika (prompted) mind is coward.

What is sasaṅkhārika (prompted)? (src)

12. Sankhārika-
    This is purely a technical term used in a specific sense in the Abhidhamma. It is formed of 'sam', well and Ö 'kar', to do, to prepare, to accomplish. Literally, it means accomplishing, preparing, arranging.
    Like dhamma, sankhāra also is a multi-significant term. Its precise meaning is to be understood according to the context.
    When used as one of the five 'aggregates' (pañcakkhandha), it refers to all the mental states, except vedanā and saññā. In the paticca-samuppāda it is applied to all moral and immoral activities, good and bad thoughts. When sankhāra is used to signify that which is subject to change, sorrow, etc., it is invariably applied to all conditioned things.
    In this particular instance the term is used with 'sa' = co-; and a = un, Sa-sankhārika (lit., with effort) is that which is prompted, instigated, or induced by oneself or by another. 'Asankhārika' (lit., without effort) is that which is thus unaffected, but done spontaneously.
    If, for instance, one does an act, induced by another, or after much deliberation or premeditation on one's part, then it is sa-sankhārika. If, on the contrary, one does it instantly without any external or internal inducement, or any premeditation, then it is asankhārika.

How can the practitioner comprehends shyness?

the practitioner must comprehends below mind, it's mental factors, and the matters born of those mind&mental factors to comprehend shyness:

4 prompted attaching mind (src)

Attaching consciousness, prompted, accompanied by pleasure, connected with wrong view,
Attaching consciousness, prompted, accompanied by pleasure, disconnected with wrong view
Attaching consciousness, prompted, accompanied by indifference, connected with wrong view
Attaching consciousness, prompted, accompanied by indifference, disconnected with wrong view

Mental factors: Twenty-two factors enter into combination - namely, thirteen aññasamānas, and 3 greed mental factors, 2 boring mental factors, and 4 ignorant mental factors (13 + 3 + 2 + 4 = 22)

1 prompted rudeness mind (src)

Rudeness consciousness, prompted, accompanied by displeasure, connected with ill-will

Mental factors: Twenty-two factors enter into combination - namely, twelve aññasamānas, and 4 angry mental factors, 2 boring mental factors, and 4 ignorant mental factors (12 + 4 + 2 + 4 = 22)

12 prompted wholesome mind (src)

Beautiful consciousness, prompted, accompanied by pleasure, associated with knowledge. x3 (wholesome, resultant, kiriyā)
Beautiful consciousness, prompted, accompanied by pleasure, dissociated with knowledge, x3
Beautiful consciousness, prompted, accompanied by indifference, associated with knowledge,x3
Beautiful consciousness, prompted, accompanied by indifference, dissociated with knowledge.x3

Mental factors: thirty-six factors enter into combination - namely, thirteen aññasamānas, and twenty-five beautiful mental factors (13 + 25 = 38)

Anupubbīkathā is an over long sutta

Ugga-richman, lay, said in Sutta. Aṅ. (4): aṭṭhaka-nipātā:

With confident heart I paid homage to the Buddha. The Buddha taught me step by step (anupubbikakathā), with a talk on giving, ethical conduct, and heaven. He explained the drawbacks of sensual pleasures, so sordid and corrupt, and the benefit of renunciation. And when he knew that my mind was ready, pliable, rid of hindrances, joyful, and confident he explained the special teaching of the Buddhas: suffering, its origin, its cessation, and the path. Just as a clean cloth rid of stains would properly absorb dye, in that very seat the stainless, immaculate vision of the Dhamma arose in me: ‘Everything(suffering) which is arise by the origins(samudaya), has an end.’ I saw, attained, understood, and fathomed the Dhamma. I went beyond doubt, got rid of indecision, and became self-assured and independent of others regarding the Teacher’s instructions. Right there I went for refuge to the Buddha, his teaching, and the Saṅgha. And I undertook the five training rules with celibacy as the fifth. This is the second incredible and amazing quality found in me.

After listened anupubbīkathā, some listener can enlighten "dhammacakkhuṃ", i.e. from DN Sāmaññaphalasuttaṃ:

So King Ajatasattu, delighting and rejoicing in the Blessed One's words, rose from his seat, bowed down to him, and — after circumambulating him — left. Not long after King Ajatasattu had left, the Blessed One addressed the monks: "The king is wounded, monks. The king is incapacitated. Had he not killed his father — that righteous man, that righteous king — the dustless, stainless Dhamma eye would have arisen to him as he sat in this very seat."

You can search more result by yourself with word "dhammacakkhu", "anupubbika" and "anupuppīka".

There are many place like that in tipitaka, so Buddha exactly taught four noble truth to the lay. The required questions are:

1. What is anupubbīkathā?
2. Why Buddha often taught anupubbīkathā to a lay?
3. Why the first saṅgāyanā monks have to separate anupubbīkathā as may partitions?
4. Why some people think Buddha never taught meditation to a lay?

1. What is anupubbīkathā?

1. Anupubbīkatha, in pāli canons, is the sequence teaching, story, or history. See, each searching results from tipitaka and atthakathā.

2. Anupubbīkathā, in tipitaka context, the single time teaching of entire instructional sequence. It is the very long sutta which describing about buddhist practitioner's procedure, such as single time teaching of KN Khu Nidhikaṇḍaṃ (with some commentary) + AN Uposathasuttaṃ (with some commentary) + DN Sāmaññaphalasuttaṃ (with some commentary). You can see that is over long to orally recite.

2. Why Buddha often taught anupubbīkathā to lay?

Buddha taught anupubbikathā to everyone, not only lay, because every practitioner must practice step by step. No one can practice without sequence like a fog. See, MN Majjhimapaṇṇāsaka Kīṭāgirisutta Number 238.

However for a newbie lay who is genius, buddha taught him from the beginning step to the end in single time, such as single time teaching of KN Khu Nidhikaṇḍaṃ (with some commentary) + AN Uposathasuttaṃ (with some commentary) + DN Sāmaññaphalasuttaṃ (with some commentary).

You can see that is over long to orally recite.

That's why we can't find the single sutta of anupubbīkathā, in tipitaka context, or even in atthakathā as well. So, in atthakathā comment of anupubbīkathā:

Anupubbīkathā is sequence of teaching and commentary of dāna subjects then sīla subjects then heaven subjects then practitioner's procedure.

But the buddha&teacher taught a shorter and more complex sutta to the insider lay man&lay woman, upāsaka and upāsikā, because they have enough ability and knowledge to learn the higher level, e.g. AN Dānasutta. You can see that sutta is shorter and more complex, included only charity and the Path. It is anupubbīkathā, but it is not the meaning of "anupubbīkathā" word in the context like Sutta. Aṅ. (4): aṭṭhaka-nipātā.

3. Why the first saṅgāyanā monks have to separate anupubbīkathā as may partitions?

The first saṅgāyanā monks chose "anupubbikathā" words to avoid the over long of sutta. Because most of lay at that time don't have much knowledge for an enlightenment, buddha have to taught them very long sutta (maybe more that DN) and mix many contents to let them enlighten as sotāpanna, or trust to dhamma. So, if the first saṅgāyanā monks didn't separate it to be many smaller sutta, it will be over long and unable to orally reciting study.

The evidence from netti vicayahārasampāta:

587. Herein, the Lord Buddha advises one of keen faculties with advice in brief; the Lord Buddha advises one of medium faculties with advice in brief and detail; the Lord Buddha advises one of blunt faculties with advice in detail.

4. Why some people think Buddha never taught meditation to a lay?

Because they are misunderstanding of anupubbikathā. And they don't know how to read teaching as four noble truth, because they never memorize netti, or never attained any professional knowledge, ñāṇa, from tipitaka-memorizer&jhānalābhī school, such as Pa-Auk.

Every noble one must enlightened four noble truth, but it is not every ordinary people can discover the noble truth from tipitaka. People who can understand the noble truth from tipitaka must can deconflict every uncleared word of tipitaka. This is unable for people who can't memorize tipitaka pali and netti, because it needs nirutti-paṭisambhidā to deconflict the whole tipitaka.

For the example from VN Mahāvagga by assachi arahanta to sāriputta, who enlightened as sotāpanna:

Ye dhammā hetupabhavā (dukkha) tesaṃ hetuṃ (samudaya) tathāgato āha
tesañca yo nirodho (nirodha&magga) evaṃvādī mahāsamaṇo.

‘Those things(suffering) which proceed from a cause, of these the Truthfinder has told the cause(origin), And that which is their stopping (cessation&path)— the great recluse has such a doctrine.’”

Or in Sāmaññaphalasuttaṃ, which king Ajātasattu almost enlightened as sotāpanna, it is included vipassanāñaṇa part (brief dukkha), pubbenivāsānussatiñāṇa+cutūpapātañāṇa (extended dukkha), āsavakkhayañāṇa (samudaya+nirodha), and all practitioner's procedures in this sutta are magga.

All above is the example of how to read the noble truth in tipitaka.

(Must read!) No lokuttara arūpa, Words' relation about lokiya&lokuttara jhāna

Therefore, lokuttara-appanā jhāna has not arūpa-state, lokuttara-nibbāna are over all aggregates, paṭicca-samuppāda cessation at all. That means there is no rūpa-object or arūpa-object for lokuttara-appanā consumer to think out of, no object for meditation, because the nibbāna-object, of lokuttara-appanā-jhāna, has already out of all aggregates.

The explanation of meditation's relative words:

Pāli words relation: The paṭipanno bhāvanā samādhi by doing jhāna of samatha-ārammṇa. The comparative of bhāvanā's paricita called (nānā ārammanāni) khaṇiko samādhi, the upacāra of samādhi to samāpatti the ekagga-bhāva, and the upacāra of samādhi to samāpatti the ekagga-bhāva. (I used all of pāli word as nāma-sadda to avoid vibhatti's variation, but ). Ekaggatā is eka-bhāva of citta that has eka-rāsi of cetasikasampayutta and eka-ārammaṇa.

The translation of above pāli words relation: The practitioner meditates concentration-meditation by watching samatha-object. The comparision of meditation's evolution called various-object-momentary concentration, almost-consummated-one-pointedness concentration, and already-consummated-one-pointedness concentration. The one-pointedness is the state of mind that has only one same set of mental factors and only one-object continuously arising.

Lokiya = Under Aggregates' Dependency, paṭiccasamuppāda.
Lokuttara = Over Aggregates' Dependency. Lokuttara-aggregates are over present&future taṇhā aggregates, and future resultants. Lokuttara-nibbāna are over all aggregates.

By Abhi. Vibhaṅgo, Samāpatti (consummation) means bhāvanā (meditation). By Mettānisaṅsasutta, it's atthakathā, and Visuddhimagga, bhāvanā (meditation) means the meditation minds continuously arise without the barrier, hindrances.

So, lokuttara-samāpatti means the consummation of lokuttara-citta meditation. And lokiya-samāpatti means the consummation of lokiya-citta meditation.

What is appanā of one-pointedness?

The practitioner meditates the meditation to be proficient (samāpatti). The professor (samāpanno) of the meditation can think of the meditation object without bhavaṅga, five hindrances, and the letting go object. This is why the one-pointedness can be the state of mind that has only one same set of mental factors and only one-object continuously arising.

What is the difference of Lokiya Appanā VS Lokuttara Appanā?

Note: this is just the comparison. But in the real situation, virtual mind&concentration mind&insight mind switch each others to arise depend on the environment of the meditation. The purified virtual and purified concentration (visuddhi) arise automatically in the proper situation because to support the Insight meditation. This is the reason why taṇhā-carita practitioner should meditate concentration meditation specially, his concentration must ready to arise automatically in the environment that five hindrances, pariyuṭṭhāna-kilesa, can arise to hinder all meditation. The concentration mind must automatically arise before the hindrances arise to destroy the meditation.

Lokuttara Appanā
Practitioner is 4 Mahākusala/4 mahākiriyā mind with 33 mental factors.
Practitioner's object is Whole five aggregates in dependent origination cycle for the appearance of three normal characteristics.
The enemy is whole future 14 arise-able unwholesome (anusaya-kilesa) especially avijjā, lobha, dosa, sakkāya-diṭṭhi.
Enlightenment is 40 lokuttara appanā minds with 36 mental factors 40 which knowing only nibbāna.
Enlightenment's object is Nibbāna-object which is the opposite of whole five aggregates.

Lokiya Appanā
Practitioner is 4 Mahākusala/4 mahākiriyā mind with 35 mental factors.
Practitioner's object is the pair enemy-object of specific present unwholesome (pariyuṭṭhāna-kilesa), such as asubha-meditation is the couple of subha-kāmarāga hindrance.
The enemy is the whole present 14 arise-able unwholesome (pariyuṭṭhāna-kilesa) especially 5 hindrances.
Consummation is 27 lokiya appanā minds with 35 mental factors which knowing only that pair enemy-object of specific present unwholesome (pariyuṭṭhāna-kilesa).
Consummation's object is the pair enemy-object of specific present unwholesome (pariyuṭṭhāna-kilesa). Some of them are the realities, some of them are paññatti:

1. Because five strings (paṇcakāmaguṇa) are variant reality at five senses, the rūpa-jhāna practitioner must think of the unlimited enemy imagination (paññaiti-object) of five string realities to avoid the five-string-reality thought. But rūpa-jhāna concentration base on the matter, the jhāna's element-pausing effort is not the cause of getting arūpa-object. The rūpa-jhāna consumer can get arūpa-object after his jhāna-power is strong enough.
2. Because out of the paused jhāna-elements, the fifth rūpa-jhāna consumer's ability is ready to think without any matter, the fifth rūpa-jhāna consumer can meditate arūpa-jhāna from now on.
3. Because every paññatti-object of rūpa-jhāna base on the collection of five strings (seven gocara-rūpa), this jhāna consumer still be easy to return to attach five strings again. So, the fifth rūpa-jhāna consumer must try to think out of every five strings by thinking of arūpa-jhāna object. Letting matter go because nothing of arūpa-jhāna object relating with matter.

Therefore, lokuttara-appanā jhāna has not arūpa-state, lokuttara-nibbāna are over all aggregates, paṭicca-samuppāda cessation at all. That means there is no rūpa-object or arūpa-object for lokuttara-appanā consumer to think out of, no object for meditation, because the nibbāna-object, of lokuttara-appanā-jhāna, has already out of all aggregates.

See this article.

Buddhist Jhanas, how to describe them?

In addition to primary sources that discuss what this phenomena is, how would you describe what the Jhanas are to a person unfamiliar with any sort of meditation practice?

Jhanas are the practice to pause the present unwholesome mind. While jhāna mind are arising, there are no any wholesome mind can arise, whole hours or whole day. Jhāna is basis of insight meditation.

How do they differ across different sects/schools?

They are same in meditation. It just difference in a few detail.

How are they viewed sociologically or philosophically from OUTSIDE the lens of a practitioner or one who believes in the concept of enlightenment to begin with?

The jhāna practitioner looks very judicious, worshipful.

TL; DR seeking primary source information on Jhanas/Dhyanas. What is their history? How do they differ across schools/sects? How would an outsider or an academic understand them?

• Path of Purification https://www.accesstoinsight.org/lib/authors/nanamoli/PathofPurification2011.pdf
• Path of Freedom
  http://urbandharma.org/pdf1/Path_of_Freedom_Vimuttimagga.pdf
• Pa-Auk tawya Monastery
  http://122.155.190.19/revata/index.php?option=com_sectionex&view=category&id=6&Itemid=108#catid8

Howto count down for enlightenment follow the end of mahāsatipaṭṭhānasutta

Is it exaggeration, translation problem or understanding problem or it's true?

The translation is fine, but the reader must know the environment and situation of that sutta, before read it. If the reader read it without the pre-required knowledge, it is the reader's fail.

The explanation

In atthakathā of MN 10 wrote:

Why Buddha taught mahāsatipaṭṭhānasutta to Kuru-people? Because they had enough ability to study the advance teaching. It's told that Kuru-people, such as bhikkhu, bhikkhunī, lay men, and lay women, always had the potential body and the potential mind because Kuru-country had the richness of temperature, etc. Their potential body and potential mind supported their wisdom power, so they can studied the advance teaching.

So, most Kuru-people were diṭṭhi-cārita, who have little dust in their eyes, according to netti desanāhāravibhaṅga.

The diṭṭhi-cārita people can attain jhāna easily. So they don't have to meditate jhāna because of their pure mind. They can enlighten at the listening moment. That's why in the end of mahāsatipaṭṭhānasutta's atthakathā wrote:

30,000 people enlightened as arahanta at the end of mahāsatipaṭṭhānasutta was taught.

therefore, the end of mahāsatipaṭṭhānasutta wrote:

Let alone seven years, anyone who develops these four kinds of mindfulness meditation in this way for six years … five years … four years … three years … two years … one year … seven months … six months … five months … four months … three months … two months … one month … a fortnight … Let alone a fortnight, anyone who develops these four kinds of mindfulness meditation in this way for seven days can expect one of two results: enlightenment in the present life, or if there’s something left over, non-return.

But for taṇhā-carita people,who have much dust in their eyes, they have to meditate jhāna, first. After they attained jhāna, they can count down for enlightenment like what buddha taught in the end of mahāsatipaṭṭhānasutta. Because jhāna can pause their five hindrances, then their "dust in eyes" state will be same little dust as diṭṭhi-carita and they are able to count down for enlightenment.

Lord Buddha and Chakravartin

Cakkavatti is a perfect king. Everybody, included Buddha, have been Cakkavatti before uncountable times.

Buddha doesn't has next life anymore, but Cakkavatti still reborn.

Recite dhamma instead of song lyric

According to the ancient therevāda buddhist tradition, the buddhist people recite > memorize > comprehend buddha's teaching. It is ears/mouth/mind-redirection from the nonsense story to the advantage story.

Why woman can't be the Buddha?

Actually, I don't want to answer like below because the feminists have resisted me before on my reply of some topic like this. I never want to attack anyone, buddha as well.
The contex of bahudhatukasutta is about the best no.1 winner (cakka-vatti/buddha/arahanta/etc.,) vs the ordinary (the follower). So, we have to look about the qualification of the best no.1 winner.
Remember: Buddhism never against female to be the best, if everything (everything is everything, everything is not something) of them can compare to the male. But by the science, history, environment, etc., it is quite harder than the male.

So, what is the qualification of the best no.1 winner?

1. The best physical body.
2. The best I.Q.
3. The best E.Q.
4. The best M.Q.
5. The best Teacher.
6. The best practice.
7. The best effort.
8. The best environment.
9. Etc.

Then answer me for these questions to get the answer of this topic:

Don't let me answer it by myself, because I can be killed by the feminists.

1. On menstrual period of every month, does a female has the best physical body compare to the other period of month?
2. On menstrual period of every month, does a female has the best I.Q. compare to the other period of month?
3. On menstrual period of every month, does a female has the best E.Q. compare to the other period of month?
4. On menstrual period of every month, does a female has the best M.Q. compare to the other period of month?
5. On menstrual period of every month, does a female has the best Teacher compare to the other period of month?
6. On menstrual period of every month, does a female has the best practice compare to the other period of month?
7. On menstrual period of every month, does a female has the best effort compare to the other period of month?
8. On menstrual period of every month, does a female has the best environment compare to the other period of month?
9. How many time of a life, that the male has bloody period?
10. How are the patients feeling when they lost their nutriment for bloody lesion? While this situation, how are their I.Q., E.Q., M.Q., effort, etc.?
11. How are the patients feeling when they stomachache by the bloody intestine? While this situation, how are their I.Q., E.Q., M.Q., effort, etc.?
12. How the doctors, psychiatrist, etc., answer my question?
13. Why Olympic separates the female competition from the male competition?
14. Etc.

Remember: Buddhism never against female to be the best, if everything (everything is everything, everything is not something) of them can compare to the male. But by the science, history, environment, etc., it is quite harder than the male.

---

Actually, it is from tipitaka, Sutta. Ma. U. Bahudhātukasuttaṃ , not atthakatha:

It is impossible that a woman should be the Universal Monarch It is possible that a man should be the Universal Monarch.

It is from Mahidol University Application Budsir The Pali Tipitaka in Roman Character Volume 20 page 36-37.
http://www.84000.org/tipitaka/read/roman_read.php?B=20&A=738

Click here for these versions of this sutta: Siamrattha(THAI), Mahaculalonkorn University, Atthakatha Pali, and Thai translation of Atthakatha by Mahamakut University.

There is no changing in practice after the unfolding of sotāpanna

The practitioner no need changing the practice.
The practitioner has to comprehends 3 characteristics of 5 aggregates, which cycling as the dependent origination, from being ordinary until arahatta-magga. But the teaching literature may be difference. See the description after the below quote.
So, in Sutta. Saṃ. Kha. Sīlavantasutta taught the same meditation for all people, ordinary and all noble one:

On one occasion Ven. Sariputta & Ven. Maha Kotthita were staying near Varanasi in the Deer Park at Isipatana. Then Ven. Maha Kotthita, emerging from seclusion in the late afternoon, went to Ven. Sariputta and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there, he said to Ven. Sariputta, "Sariputta my friend, which things should a virtuous monk attend to in an appropriate way?"
"A virtuous monk, Kotthita my friend, should attend in an appropriate way to the five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. Which five? Form as a clinging-aggregate, feeling... perception... fabrications... consciousness as a clinging-aggregate. A virtuous monk should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. For it is possible that a virtuous monk, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of stream-entry."
"Then which things should a monk who has attained stream-entry attend to in an appropriate way?"
"A monk who has attained stream-entry should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. For it is possible that a monk who has attained stream-entry, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of once-returning."
"Then which things should a monk who has attained once-returning attend to in an appropriate way?"
"A monk who has attained once-returning should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. For it is possible that a monk who has attained once-returning, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of non-returning."
"Then which things should a monk who has attained non-returning attend to in an appropriate way?"
"A monk who has attained non-returning should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. For it is possible that a monk who has attained non-returning, attending in an appropriate way to these five clinging-aggregates as inconstant... not-self, would realize the fruit of arahantship."
"Then which things should an arahant attend to in an appropriate way?"
"An arahant should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. Although, for an arahant, there is nothing further to do, and nothing to add to what has been done, still these things — when developed & pursued — lead both to a pleasant abiding in the here-&-now and to mindfulness & alertness."

But the teaching literature may be difference. Each enlightenment depend on each personal understanding-ability because each person has difference own understandable dhamma, i.e. Pañcavaggī were professional of aggregates before he meet buddha, but Dīghanakha were professional of six sense fields before he meet buddha, etc.

• Dīghanakha enlightened nibbāna as sotāpanna by comprehending 3 characteristics of the dependent origination (nāma-rūpa) in Sutta. Ma. Ma. Dīghanakhasutta.
• A thousand jaṭila enlightened nibbāna as arahanta by comprehending 3 characteristics of the dependent origination (six sense fields, six contacts, six feeling) in Sutta. Saṃ. Saḷa. Ādittapariyāyasutta.
• Koñḍañña-pañcavaggī enlightened nibbāna as sotāpanna by comprehending 3 characteristics of the fourth noble truth in Sutta. Saṃ. Ma. Dhammacakkappavattanasutta.
  • All pañcavaggī enlightened nibbāna as arahanta by comprehending 3 characteristics of five aggregates, which is continuous from the five clinging-aggregates suffering noble truth of Dhammacakkappavattanasutta above, in Sutta. Saṃ. Kha. Anattalakkhaṇasutta.