The main problem with this discussion is that the major modern Indian languages are not stressed languages at all. If you hear these names spoken in traditional settings, they will be stressed depending on the sentence context: `Kavita, do this' and `Kavita did this' will seem to carry different stress patterns (this is true for most languages), and the only stress that you hear is the stress arising from the sentence pattern (this is specific to unstressed languages).
That said, the *length* of vowels in many (but not all) of these languages is meaningful, as is the duplication of consonants. I know of no language (doesn't mean it does not exist) where the -i- in Kavita is long, nor one where the -t- is doubled. And, note, I am talking only of these names pronounced traditionally in India.
The first two vowels in kavitA are short: the first is like the a- in English about and the seconds one is as in hit. The last one is long like in car. In mIrA, both are long: the last one is same as in kavitA, and the first one as in English heat. The k- and m- is the same as the corresponding English sounds, the v- is a labio-dental (touch the upper teeth to the lower lips: less breath than in English v- and a slightly different shape than English w-). The t- is dental unaspirated unvoiced (i.e. the tongue touches the teeth, much closer than English t- in talk, much less breath than English th- in thing, unvoiced *unlike* English th- in the). The correct pronounciation of the -t- is important since the phonetic differences from English there have phonemic value in the North Indian languages (where this name has meaning). The English r- is pretty close to the r used in mIrA.
The exact pronounciation of the vowels and consonants also changes from language to language. What I described above is the so called Hindi belt pronounciation.