Not really....but in someways yes (it depends). The prakrit(s) we know about (evidence wise i.e written mostly and some analysis of spoken languages today) are descendants of the earlier sanskrit/"prakrit" that would have existed in the Vedic era.
Only the sanskrit from that era (
I have been referring to this as Indo-Aryan, to distinguish between what there was, and the codification of Panini) was preserved (orally/aurally) because it was the highest register of the language (and designed specifically so there was little to no chance of mistakes happening in the mouth to ear learning system the earliest priests/bards devised, given the word sounds themselves were considered Word of God...i.e Sruti).
There would of course have been a more laypeople language used by the broader population in that time...which would qualify as what we call prakrits later. There is of course no evidence as to how it sounded given it was not passed in that time (where there was no writing, only spoken+hearing record that preserved the highest register for religious purposes...i.e what we call Vedic Sanskrit).
Again Sanskrit is simply
the highest register of the indo-european language that predated written Prakrit (= Indo-Aryan) Bengali is definitely a direct descendant/relative of all (Vedic Sanskrit, Vedic Prakrit, Classical Sanskrit, Classical Prakrits and all their earliest descendants) of it....it is an Indic language, which is major branch of indo-european family. Just we have no direct idea about what Vedic "Prakrit" was like...it just has not been preserved in the oral tradition of that time (only vedic sanskrit was).
Specifically, linguistics distinguishes between western versions derived from Suraseni Prakrit, and eastern versions derived from Magadhi Prakrit. We can say that Bengali is finally descended from Magadhi Prakrit. As is Assamese, Odiya, and Nepali.
That is just vedic sanskrit (specifically the meter, which is precisely designed and thus has poetic forms in prakrits, descendants and Hindustani etc). Classical Sanskrit is more vernacular use, thus does not have this "meter" in same way (though it is found in most major compositions etc) :
https://en.wikipedia.org/wiki/Vedic_meter
Vedic Sanskrit after all is not very layperson friendly...in fact that is why classical sanskrit was later developed and codified (and even that is not very layperson friendly either but it does have direct links to most official registers today of the indic languages).
Vedic sanskrit is like it is by origin/design/meter (whatever combo you believe) to basically preserve the sound
exactly. You have to learn at least one Veda to really know why (the process also has many specific tools like memorizing back to front and front to back equally in word order, so to prevent any chance of mistake, much like a code checker)....its not flexible to be used to write/speak new things/ideas...even new grammars/shortcuts/innovations. That was the purpose of classical sanskrit (and of course prakrits which is even more easier given it basically took the form of the local influences wherever it was). Classical sanskrit itself took much influence from Dravidian languages it is increasingly being found (and vice versa).
Rest I will let Joe answer
for Bengali script pronounciations of Sanskrit. You are right that English will do a lousy job.
Are you saying the transliteration and translation are exactly the same (into Bengali)? Bengali (And all prakrit descendants) has all the script it needs to capture Sanskrit (all indic languages essentially do) I think...but not 100% sure. Joe would know more on this I think. I am only familiar with devanagari (and grantha) for written sanskrit (be it Vedic or Classical).
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