Don't think anyone will be able to give you really clear responses to your questions, but I'll give it a whirl. FWIW, I'm an Indian male reapplicant as well and was on the waitlist of a different school last year for 6 months. I did get into a couple of schools in R1 this year, Tuck included.
1) I don't think you'll find any clear information about this anywhere. It will depend every year, but this link by MBA Data Guru should give you some insight. Please note that the conclusions might be flawed because its completely dependent on self-reported data.
http://www.mbadataguru.com/blog/mba/mba ... 2019-data/2) Based on previous years, looks like it could be any time. Typically best times to look out are during R2 decisions and during deposit deadlines. It could also only happen after R3. I don't agree that a lot of people decline their offer, Tuck really tries to make sure that the people they admit really want to be there. Their yield is around 50% and has held pretty steady. Also, people pick Tuck over M7 schools regularly because of its culture. Anecdotally, I know someone who was waitlisted at Tuck in EA and didn't make it in at all.
3) I did some coursework while I was on the waitlist and I wrote a letter of interest aside in addition to the measures you mentioned. It still wasn't enough to get me off the waitlist despite a pretty major improvement of my GMAT score. I did visit the campus this year to interview and I think it was the best decision I made. However, I'm fairly certain they don't expect you to do it from India. The cost is pretty significant and there is no guarantee it will move the needle or make any difference to your waitlist decision. You might be better off spending that time and effort on your R2 apps, but its your call.
This is just based on my experience as a reapplicant to Tuck and as someone who's been on the waitlist, I'm absolutely not an expert. Take everything I've said with a grain of salt and maybe speak to students at Tuck to get a better idea.
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