How do we guarantee the accuracy and validity of Buddhist scriptures? In this site participators draw statements from &quot;Buddhist scriptures&quot; (Suttas), considering them pure and directly from Buddha's words.
Some of these statements [seem] closer to fantasy, supernaturals, assumptions and speculations; and few are false statements (e.g &quot;thoughts are generated in heart&quot; is mentioned in Abhidharma). Also information extracted from Buddhist scriptures are mixed with Hindu concepts as milk and water (most of original Buddhist scriptures were destroyed in Thakshila). In the kalama sutta it mentions that to completely depend on scriptures is useless.
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? 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?

Here's another example:

Then Ānanda, listen and attend carefully, I will tell.
The Blessed One said: Ānanda, as long as the moon and sun illuminate the directions, till then the thousandfold world systems will prevail, with a thousand, moons, suns, Mahameru mountains, Indian peninsulars, Aparagoyanas, Uttarakurus, Pubhavidehas, fourfold oceans, fourfold rulers, fourfold guardian kings, heavens of the thirty-three, heavens of Titan gods, heavens of happiness, heavens of the gods of creation, heavens of the gods who create others, worlds of Brahma. Ānanda, to this is called the thousandfold Cūlanika world system. Ānanda, as long as the thousandfold Cūlanika world system prevails till then the thousandfold world system, calls this the two thousandfold middle world system. Ānanda, as long as the two thousandfold middle world element prevails till then the thousandfold world system calls this the three thousandfold and the great thousandfold world system. Ānanda, if the Thus Gone One desires, he announces to the three thousandfold and the great thousandfold world system.

These statements in suttas are closer to fantasy and speculations. How do you explain these with modern cosmology?
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.