Exam

PUMBA strictly follows the DTE rules for its admission process of MBA+.
For Maharashtra candidates, students have to qualify MH-CET exam. For Outside Maharashtra Candidates (OMS), students can apply through CAT/MAT/ATMA/XAT/MH-CET.
http://fileserver.mkcl.org/mba2017/CAP-II/2017MBA_CAP2_AI_CutOff.pdf?d

From IIM A, most probably, yes. IIM Bangalore can be tricky. Depending on your work ex. (I wouldn't count on IIMB) also there is a 80% cutoff for 10th and 12th marks, if I am not wrong.

Please use Shiksha Call Predictor, it would give you a better idea. Try and score the highest, I don't think you would want to score a 99.1 percentile instead of 99.9 percentile just because it is only as much as you need. I hope you get my point.

Check the official admissions page of PGDISM, IIM Bangalore.

As per the college Website, they only accept September or December MAT.

No, it is not possible to join MBA without giving entrance exam in Mysore or in any state or college, because every entrance exam takes the ability of a student that he she is able of studying the course which he or she is opting for.

Well, you had a good scope of getting one of the top 5 IIM, because you are 90 + in CAT, which is the main, so we hope that you get the best IIM like IIM a b or c.

Yes, you can. Make sure if you are using staedtler, then don't use water. Use them as dry colors.