IIM Bangalore - Indian Institute of Management

To seek admission into IIM-B you need to score at least 50% marks at graduation exam and must get 98+ percentile score at CAT. You also need to perform well at the personal Interview (PI). However, the percentile required will depend a lot on the score of other students as well.

Yes, you can. Since, you are pursuing B.Sc in stats and MBA in data analytics, it would be an advantage for you.

Admission into MBA without CAT/open test will not lead you to a good college and also will not be of much utility from career perspective.

MBA is not offered in IIM-A. It offers PGPM.
Refer the link to know the details:https://www.shiksha.com/mba/course/post-graduate-program-in-management-indian-institute-of-management-ahmedabad-vastrapur-1653.

IIMB uses multiple parameters, namely academic performance in school, high school and graduation programmes as well as candidates scores in CAT/GMAT to judge the suitability of candidates for the PGP programme. Relevant work experience, if any, is also given weightage. And as per the eligibility criteria candidates much have passed his/her degree with 50% marks, for sc/st it is 45%. For admission candidate has to pass CAT common admission test) conducted by IIM Bangalore.

You should target 99+ for IIM's. You might get a call from FMS with 97-98 percentile.

There are chances, if you are a non-engineer with a 99+ percentile. It is much more difficult, if you are an engineer as that would require a very high percentile in order to stand at par with other candidates.

It is highly unlikely to be honest. All the best anyhow.