IIM Ahmedabad - Indian Institute of Management

First, you have to go through CAT. For more information, visit www.iimcat.ac and also www.iima.ac

Yes, of course. But resume is considered for eligibility. Your resume should be strong with your perfect score. First 50 rankers get called from all IIMs.

You have a decent profile and especially you have a great chance at C & L as they put relatively less weightage on your graduation score.

Depends on your year's admission criteria (check the past statistics, a quick google search will throw up the result). But, I believe you should focus on CAT and think about this once you have crossed that hurdle. All the best.

IIM's I would say aren't the end of the world and you can very well reach similar or greater heights in your career despite the IIM tag. You can look at other Indian MBA B - Schools or Foreign B-Schools, that don't give as much weightage to 10th and 12th percentage like ISB.
Also, I would say it is important that you introspect a bit about your career and look for ways to progress where your past profile would not be a hurdle.

There is no minimum score as such (B has >80% criteria, might have changed so do check)
Put in your best effort for CAT, all this comes later, and you anyway can't change your scores.

Yes, but you need to perform well in GD-PI too.

IIM-Bangalore has some strict percentage criteria for boards (80% above in 10th and 12th, if I am not wrong). So, B might be off the books, but you still seem to have a decent chance at C with a high percentile. I don't want to be blunt, but you will really need to nail CAT hard. Otherwise, try looking at ISB, etc. wherein the admission isn't so marks based.
Good luck.

By now you would have understood if your interest lies in engineering. In case you have any interest and you want to pursue engineering as a career then GATE is for you. In case you like management then CAT is for you. But just to let you know, at any stage of life management is necessary, hence having an MBA degree and learning from it would always benefit you irrespective of your career path.

You can pursue your executive MBA in any of the top B-schools in India, may it be IIM A or ISB, all are at par with each other. You will get the required push forward for your career and the right people to mingle with to get your grey cells working. Personally, I would recommend PGPX offered by IIM A.