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.

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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.

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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.