Science

Yes, you are eligible for B.Sc Agriculture, and you can also get good government college. My best wishes are with you.

The admission process for PG courses of DU affiliated colleges is organized by DU itself. 50% of the seats are fill up on the basis of merit and rest through entrance. Hence, you have to first register yourself with DU for MA/M.Sc (Math) program. Further in LSR college, MA (Math) program is available and the cut off for this year is closed at 84.84% in your category.

No, there is no any college which provide M.Sc via distance.

Nautical Science is not in MIT for further details-
http://www.mitindia.edu/en/courses
All the best for your bright future!

In India, some of the places with a good Ph.D. programme are IISc, TIFR, JNCASR, RRI, RRCAT, HRI, IITB, IITM etc. See how much of work in your chosen field is being done in these universities and decide to apply if you are satisfied.

Dear Chaitanya,
The best topic for statistics project at the graduate level are :-
1. Human Statistical Genetics Research Background And Aims.
2. Bacterial Statistical Genetics Research Background And Aims.
I hope this helps you.
Thanks :)

Candidates who have qualified Bachelors Degree either in Physics, Chemistry and Mathematics combined or in Physics Honours or with B.Tech in Electronics/ Electrical/ Mechanical/ Computer are eligible for m.sc. physics
https://www.google.co.in/amp/s/www.shiksha.com/science/course/amp/m-sc-in-physics-jawaharlal-nehru-university-mehrauli-delhi-268839
you can also visit website for further details.

Material, biochemistry, energy, biomedical
Bits, DU , GU

It's good. There are a lot of scope for environmental science and eco nowadays as every public and private sector keeps an evironmentalist for the protection and avoiding deterioration of the environment and if comes to economist, they are needed in many fields and seeing your physics background, its quite good.