IIM Ahmedabad - Indian Institute of Management

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.

Please mention your category. If you are a general category then your HSC marks can play foul to your admission. Anyways, try to score high in Bachelors to get a call. Also, try to score high in CAT.

Yes, because IIM's consider the academic performance of SSC and HSC as well. So, your dip in percentage in 12th will be a negative point in that case.

IIM-A and IIM-B offer only general MBA, there is no specialisation although you can take electives in particular field to augment your knowledge of that.
The fee structure of PGDM (i.e. MBA) is generally 20-25 lakh rupees (changes every year).

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.