Answer of "How do we guarantee the accuracy and validity of Buddhist scriptures?"

How do we guarantee the accuracy and validity of Buddhist scriptures?

We guarantee it by the mukkhapātha tradition and inherit study tradition of ancient theravāda society. We strongly keep these traditions through over 2600 years of buddhism's lifetime.
There were too many rules in vinaya, suttanta, and historical evidences showed the ancient theravāda tradition has being serious to protect the original pāli cannons by reciting and memorizing.

Some of these statements [seem] closer to fantasy, supernaturals, assumptions and speculations;

How do we guarantee that fantasy, supernaturals, assumptions and speculations in sutta are not buddha's teaching?
Buddha was not Galileo Galilei, who died because of annihilationism. Buddha teaching is in the middle of eternalism and annihilationism. So, until the fantasy, supernaturals, assumptions and speculations can be possible by the logics, causes and effects or dependent origination (not only by sensual evidences), no need to deny them all.

and few are false statements (e.g "thoughts are generated in heart" is mentioned in Abhidharma).

It is just the western bad reading and studying system that make misunderstanding like that.
The fact is nothing conflicted between "thoughts are generated in heart" of abhidhamma and "thoughts are generated in brain" of biology.
Because abhidhamma taught "thoughts are generated in heart, and that thoughts (and kamma, utu, āhāra) generating brain (cittajarūpa), too".
So the psychology:

positive thinking has a lot of health benefits.

And the medical profession:

Most of the tension that occurs in your brain comes from negative thoughts that ruminate in your head.

If you have the question more about the vegetative state or the amnesia-patient, see my answer in this topic.

Also information extracted from Buddhist scriptures are mixed with Hindu concepts as milk and water.

The buddhist scriptures trying to fix the problem formed from Hindu concepts. But you biasing. So you concluded and decided like "Buddhist scriptures are mixed with Hindu concepts as milk and water".

(most of original Buddhist scriptures were destroyed in Thakshila).

You were wrong. Buddhist scriptures keeping by mukkhapātha tradition]1 and inherit study tradition of ancient theravāda society. So, where is ancient theravāda generation, there is Buddhist scriptures. Therefore, fire can't burn ancient theravāda's buddhist scriptures.

In the kalama sutta it mentions that to completely depend on scriptures is useless.

In vinaya rules, kīṭāgirisutta, too many sutta^[1][2] and ancient tradition, buddhist people must recited, memorized, and understood pāli scriptures. So, you are misunderstood kalamasutta. In ancient theravāda tradition these whole scripture evidences must not conflict each other because while reciting the answer will appear in each evidence context. Who misunderstood them as conflict each other, he showed himself that he never recited, memorized, and understood tipitaka.
For kalamasutta, it's context already showed "don't just blind faith in scriptures, but comprehension the fact benefits that you can get from the scriptures".

So how it can be verified statements exactly from Buddha himself (not as a label or maintain faith) just to get progress of right learning and confidence?

Act like buddha taught in kālāmasutta:

1. Practice yourself to translate whole pāli scripture, included abhidhamma, commentary, and sub-commentary.
2. Aovid from the other's translation,
3. but listen them all as much as you can without any bias, although you never ever trust them.
4. Decide them when you perfectly and completely studied and understood their aspect and evidence.

In my experience, I studied pāli then recite, memorize, and comprehension some important sutta by myself before decide to translate each word meaning in each sutta.
I read commentary directly. I study very simple parts of science, biology, physic, and chemistry.
I often make research of the anti-abhidhammist's evidences.
So, I still stand by the ancient theravāda tradition with a very strong decision, because I still trying to listen and prove every evidences which I can from every teachers, not just the ancient theravāda tradition teachers, and the best benefit still being in ancient theravāda tradition.

Buddhism has history of 2500 years, and scriptures were produced around 300 years after death of Buddha. So how do we guarantee the accuracy and validity of thousands of Buddhist scriptures?

The physical scriptures produced around 450 years, but the study system produced from buddha's living time. You can make your own assumptions. But I will trust just the evidences, history, and appearing culture.
Why the western buddhist professors and students usually stand by the assumptions more than the evidences? Because of their bias about the suffering, such as Crusades or dark age, from their ancient religious, right? Do they forgot that buddhism is not their ancient religious?