MBA/PGDM

Yes, you can definitely take admission in the 2019-2021 session. All you need to do is to contact the college that you are applying to and need to update your scores as and when it is declared.

Yes, you can do MBA, but not M.Com.
You can do MBA because it's a multidisciplinary course, whereas, M.Com, you can't as it's a general course for which you need to have a basic knowledge of accounts.

Yes, I am 85 percent sure you'll be able to convert, rest depends on the GDPI.

Instead of distance, I would rather say that you should pursue a full-time course as a full-time course will gain you lots more knowledge and you'll be able to secure good placements.
Some good colleges are:
Great Lakes, Chennai
Jain University, Bangalore
Rajagiri Centre for Business Studies, Kochi
Pune University
NIT-Agartala
LIBA, Chennai
ISB, Hyderabad.

You can apply for colleges like:
BIMM
ISBS
ITM Navi Mumbai
RIIM
Jaipuria. Etc. I am currently studying in BIMM Executive (marketing).
For more queries, or discount in form filling, comment below.

Yes, you can. You can fill form for colleges like:
BIMM
ISBS
ITM Navi Mumbai
RIIM. etc. I am currently studying in BIMM Executive (marketing)
For more queries, or discount in form filling, comment below.