M.Sc

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/

Yes, definitely, you can do it. But rather, try for MD Biochemistry where you will get more wider prospective in teaching Biochemistry. All the best.

Please click the link below for all the details related to pattern and syllabus for the entrance exam of M.Sc
https://www.shiksha.com/science/articles/how-to-prepare-for-top-msc-entrance-exams-blogId-13489

Below are the colleges that offers integrated M.Sc. And Ph.D. course for biological Science:
1. NISER
2. NMIMS University
3. NCBS.