I agree with the others, it is better to have the medical done at least a week or two before the interview, just in case. That said, I know of a few people who did get their medical done the day before the interview, with no problems. (My husband took the train from Hyd to Chennai for the medical; then again traveled to Chennai for the interview weeks later.)
The original interview letter is generally required. They want to see that before they let you into the Consulate on the day of the interview.
I have never heard of a case of the visa given the same day in Chennai.

A few people have gone to the VFS office the next day and got it in person. Otherwise, it is sent by courier and generally arrives within 3-4 days after the interview.