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

The basics of Buddhism is the Triple Refuge. The 2nd Refuge is refuge in the Dhamma or the Teachings, which is officially & completely defined as follows:

Svākkhāto bhagavatā dhammo sandiṭṭhiko akāliko ehipassiko opaneyyiko paccattaṃ veditabbo viññūhīti

The Dhamma is well expounded by the Blessed One, directly visible, immediate, inviting one to come and see, applicable, to be personally experienced by the wise.

Everyday, the above verse is chanted in every Theravada monastery by the monks & nuns. Anything that falls outside of the above definition of Dhamma is not the True Dhamma.

The only people with right learning & confidence are Stream-Enterers & above, who have experienced which teachings when practised result in Nibbana (freedom from suffering).

As stated in the Kalama Sutta, Buddhism does not have any expectations of unverified belief.

Buddha expounded 84000 different teachings to suit the different types of personality and background. So if one starts exploring, one will find the champion teaching. It is like different cultures in different country. In one country people like durians, but in another country, people find eating durians too disgusting. Thus, one need to find the teaching that suits- not necessarily from reading but also from hearing a Sangha.

Wisdom needs to be balance with faith. Too much faith in only materialism and only what can be proven to the world is a recipe for one lopsided and heartless religion that is not very good at cultivating peace and happiness for it's congregation.

Those with no faith will probably not find the value in the Eightfold Path.

Any relationship to the Vedas or Brahmin concepts is usually the Buddha making fun of those concepts or twisting them around to make a different meaning.

There are no guarantees. The scriptures are merely guidelines to show how one can practice to make good habits and undo bad habits for the purpose of getting what every human being wants at the end of the day: Happiness and peace.

The more a certain teaching of the Buddha is repeated throughout the suttas, the more likely that certain teaching is an authentic teaching from the Buddha. I suppose that is just common sense.

May we all find peace and happiness and be overflowing with metta in all directions...

Several answers.

First is the Sangha. If I have question about Buddhism, about what a sutta means, I'd want to look for some other peoples' opinions of it first, before my own.

The sutta you quoted (AN 3.80) is not translated on AccessToInsight nor on Dharmafarer (though it is on SuttaCentral).

I only infer from that they consider this sutta to be relatively unimportant, not the most essential sutta -- see also the topic Chronological or other sequence for beginners on this site.

Academics have tools to try to answer this question. There are academics who investigate whether things were really written by Shakespeare, for example, or whether a painting is by Da Vinci. I think a good example of that is the (academic) paper which I referenced and summarise in this answer.

See also Which suttas in the Pali canon are relatively early or late?

The Buddha himself is said to have given an answer to this question. From the Maha-parinibbana Sutta:

Then the Blessed One said: "In this fashion, bhikkhus, a bhikkhu might speak: 'Face to face with the Blessed One, brethren, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation'; or: 'In an abode of such and such a name lives a community with elders and a chief. Face to face with that community, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation'; or: 'In an abode of such and such a name live several bhikkhus who are elders, who are learned, who have accomplished their course, who are preservers of the Dhamma, the Discipline, and the Summaries. Face to face with those elders, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation'; or: 'In an abode of such and such a name lives a single bhikkhu who is an elder, who is learned, who has accomplished his course, who is a preserver of the Dhamma, the Discipline, and the Summaries. Face to face with that elder, I have heard and learned thus: This is the Dhamma and the Discipline, the Master's Dispensation.'

"In such a case, bhikkhus, the declaration of such a bhikkhu is neither to be received with approval nor with scorn. Without approval and without scorn, but carefully studying the sentences word by word, one should trace them in the Discourses and verify them by the Discipline. If they are neither traceable in the Discourses nor verifiable by the Discipline, one must conclude thus: 'Certainly, this is not the Blessed One's utterance; this has been misunderstood by that bhikkhu — or by that community, or by those elders, or by that elder.' In that way, bhikkhus, you should reject it. But if the sentences concerned are traceable in the Discourses and verifiable by the Discipline, then one must conclude thus: 'Certainly, this is the Blessed One's utterance; this has been well understood by that bhikkhu — or by that community, or by those elders, or by that elder.' And in that way, bhikkhus, you may accept it on the first, second, third, or fourth reference. These, bhikkhus, are the four great references for you to preserve."

The Abhidamma isn't the same as the suttas. Both the Abhidamma and the Suttas are parts of the Tripitaka (the Pali and/or Theravada canon), but I think there are Buddhists who prefer the suttas.

Beware of translations. A word like "Heart" or "World" or "Atom" has a modern meaning. When suttas are translated into modern words, they may seem to make less sense (e.g. because you don't think with what you'd now call a "heart"). Consider though that the statement probably made sense in the original time and language, and that the translation is an approximation ... it's partly up to you to try to understand what it meant originally. It's also well to recognise that there are several translators and translations, some may make more sense to you than others.

A reason why you may find Buddhism interesting is that it's helpful, useful, and self-evident (by which I mean that it make statements which accord with your own experiences).

So take the parts of it that you find helpful.

It's worth studying what the suttas actually say, I think they're carefully expressed.

For example you wrote,

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

The Kalama Sutta might say something a bit like that, but it doesn't say exactly that. I think it's worth considering exactly what it does say.

I've seen at least one "cosmological" sutta (the Aggañña Suttaa) described as being a parody of the Vedas, or as Buddhist mythology (I guess that's a matter of opinion which some other people would not agree with).

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?

I think you are forgetting that those world systems, mythology about the creation and evolution of man, gods, Brahma, etc. were all 100% real to the people of the Buddha's time based on what information they had. If it makes it easier for you, feel free to reimagine them with the scientific terminology of today. My expectation, however, is that in 2,500 years, all of those cutting edge theories are going to seem at little quaint, dated, and mostly likely wildly, wildly wrong.

What doesn't change, however, are the core principles of liberation. These are not dependent on any creation story (as the truths of, say, Christianity are) but are instead derived from direct insight into how suffering is caused by craving. While you are unlikely to meet any Nagas anytime soon, you are guaranteed to find yourself facing down all of the obstacles to liberation mentioned in the suttas. The means given for overcoming them will also remain valid so long as there are humans able to hear them.