M.Sc

It would be better, if you directly contact concerned university, so that you may be able to get your certificates.

Yes, you are eligible for the same.

Admission procedure starts in February.

Yes, you can do the same.

Yes, you are eligible for the same.

In Kerala University:
Eligibility: Student who has passed Bachelor's Degree and intermediate in second division with at least 50% marks separately in both and must have offered the subject at graduation level in which he/she is seeking admission.

Christ University
Oxford college of Science
Bangalore University
JNCASR.

Yes, it does have huge value and great prospects for a campus placement. In today's times what matters more is an institute. JB has a huge brand value. It will add so much credibility to you.
Moreover the course is very rigorous and relevant from industry point of view.
Go ahead and be a JB-iite - http://jbims.edu/placements/final-placements/msc-finance/