CMAT

Hello,
You may refer the link below that gives you a list of more than 50 top MBA colleges in India that offer CMAT scores:
https://www.shiksha.com/mba/colleges/mba-colleges-accepting-cmat-india

In my opinion, CAT is better because no. of colleges accepting CAT scores are slightly more than accepting CMAT. But there is hardly much difference.

CMAT is given priority at the time of admission but you can also get admission on the basis of your attempted exams.

Not only CAT or CMAT you can also attempt other examination like MAT XAT etc as it is compulsory for admission in the college and every college has their own policy for selecting the candidate through the entrance exam.and your national sports certificates will be a attraction but not a concession.

Bleak chances for MMS. But you can apply for PGDM AIMA if you haven't applied for core PGDM.

Easily, you can admission in the BK School Of Management with 2016 and you can apply through the college website asap.
Admission is based on the score obtained in CMAT/ GCET (Gujarat Common Admission process for B K School of Business Management)
All the best.

No, it does not accept CMAT score.

Yes, you can prepare for CMAT along with it.