Hi Sohini!
You have a solid profile! Let me answer your primary queries, but happy to chat more.
1. Absolutely! While the average is about 5 years of experience, you are definitely not on the higher end. In fact, having more work experience before going to MBA will really help you well with landing a internship/post-MBA offer. We can even use optional essays to highlight your IIT and GMAT scores.
2. Foster, UCLA, USC Marshall on West coast would be good bets to transition into product management due to geographical proximity to tech companies. Other schools I'd consider are UNC, McCombs, Emory, Kelley. You can even get strategic and go after some of the Top 10 schools with high admit rates and good product management placement history. Insead and Cambridge are good options outside of US, but if I were you I would choose US given your post MBA goals around product management.
3. I am an alumni from UNC Kenan Flagler, currently working as a Global Product Manager at Amazon. I have helped candidates last year to get into McCombs, Kelley, Foster, UCLA, UCI, Cornell, and many more. A bunch of them got pretty good scholarships as well.
Given our backgrounds, I genuinely believe that I'd be able to help you land some good schools. I sent a PM with additional details to see if you'd be interested to get on a call. I am happy to connect you to a couple of other candidates that I am helping at the moment to see if our working style works for you.
Best,
Chandana