B.Sc

It is not actually necessary. If you want to live in a private room you can do that too.

You may or you may not. Every college has its different guidelines, so contact to your desired college.

You have lot of time. Firs, complete your B.Sc.

Yes, IIT Jam is a good option, otherwise you can also give entrance for BHU for M.Sc Mathematics. BHU is also one of the best colleges of India.

You should consult with admission authorities of your institute whether you can get lateral entry. Having a good academic record will also help to secure admission. You should block a seat in the college you want to study before giving up your seat in your current college. Institutes normally allow lateral transfers under special circumstances like medical issues, shifting base from one place to another, etc.

Eligibility for MBA program: The prospective applicant must satisfy one of the following eligibility criteria for admissions to the MBA program. A graduate degree under 10+2+3 or 10+2+4 pattern under any discipline, securing at least 50% marks in aggregate, from a recognized university.
However, different universities have different admission criteria and you should check with the admission authorities of the target institute for eligibility criteria for a course in their MBA program.