Yeah, although the word “Sanskrit” (Skt. “sa.msk.rta”, where dot-before represents dot-under, indicating the nasalization and vocalic “r” respectively) does mean “perfected”, it’s rather strange to see it described as “unambiguous”. Ambiguity is the heart of elegance in Sanskrit, which (kind of like German, but much more so) frequently uses long compound words in place of multi-word phrases or clauses. The more different meanings you can combine in a single compound, the better a Sanskrit writer you are. 
Sanskrit was indeed much more grammatically and phonetically sophisticated at a much earlier date than any other language I know of. (Modern Western linguistics was actually inspired by European encounters with traditional Sanskrit grammatical works, and Sanskrit is the only language I’ve ever heard of that has a phonetically arranged alphabet—vowels come first and then the consonants in “anatomical order” of sound formation. Very sensible and intuitive system once you get used to it; you can spot a Sanskritist by asking them to look up an English word beginning with “u” in an English dictionary and watching them automatically turn to the beginning of the alphabet. :D) But the idea that “NASA scientists” think that it’s “the best language to use with computers” is at least pretty garbled, and probably a complete misunderstanding. Lots of scholars have pointed out that Sanskrit grammar is more logically consistent than that of most living languages—in fact, it is similar in many ways to modern formal language theory—but that hardly means that we should make a computer language out of it.
As for its age, “Vedic” Sanskrit (in which the Vedas were composed) is at least a few thousand years old, but it’s hard to say when it crystallized into a distinctive member of the Indo-Iranian group. By the end of the first millennium BCE it had changed significantly from the earlier form to become what is now called “Classical” Sanskrit, which was codified by the grammarian Panini sometime before the current era.
That form of the language is what has been preserved with comparatively small changes for about 2500 years to the present day, largely because it’s been a learned language rather than a “living” one or “mother tongue”. (Though my first Sanskrit professor did say that there are maybe a couple hundred people in some Indian village who speak a Prakrit or vernacular that’s close enough to Classical Sanskrit to be technically considered the same, so if you really stretch a point you could call Sanskrit a living language too.) However, millions of people still study it (mostly in Indian secondary schools), so it’ll probably be around for quite some time even if we don’t all end up writing code in it.