IIM Bangalore - Indian Institute of Management

IIM Bangalore anyday. It has a smaller batch size, is older, better climate, better placements (more offers from consult firms and banks), better faculty, surrounded by startups and MNCs.
Hence, IIM Bangalore hands down.

As of now, there isn't. Although there is a part-time MBA offered in general MBA that is for experienced candidates.
You might like the full-time course more, as it teaches you a lot more and you can get into much better roles than that from any part-time MBA program.

It is very difficult for anyone to answer this question. If you enjoy working on complex problems, putting in hard work, networking with others, playing with numbers, or in general taking a larger perspective on things, then you would enjoy the future. On average if you are looking for a career in management then IIM-B is among the top institutes and the packages also among the highest. So yes, it can increase your chances of getting a fatter pay check.

Based on your credentials, I would say that it is not impossible but you need to score more than 99 percentile in CAT exam to get admission in IIMs.

IIM nearly Impossible but for other colleges to is difficult. What about our entrance exam marks? Please share that too.

Since you did B.Com as a distance learning course, I will suggest you work for some time so that you know the reality of the job market and the corporate world, instead directly jumping into an MBA college. This will provide much-needed perspective.
For predicting if you would get a call or not check using Shiksha Call Predictor.

Shiksha call predictor should be really helpful for you, although 32.6% in 12th might make you ineligible to apply for the top 3 IIMs.

Check Shiksha call predictor. It should be near to 90%ile marks.

You need to get very good CAT %ile.