M.Sc

You can go for M.Sc from BBAU or LU from Lucknow. Both conduct entrance exams for M.Sc.

Only ranks up to 1000 can apply for an online counselling, so you can directly contact the university student counsellor.

Yes, it is a good decision to pursue M.Sc Maths in IIT. Pursuing M.Sc from IIT brings you a heap of opportunities. You can become a lecturer in IIT coaching classes. There is an institute in Delhi which deals with Quadratic Equations. It is a research institute. It requires M.Sc graduates. You can still get a good job in Google.
All the best.

The ast date of online application submission is 20th June.

Please refer to the link below for fee structure. Ths is for all students, however, you can get in touch with the university to know about the special fee structures for quota:
https://www.uok.ac.in/Fees-Structure

Yes, MBBS is there in MS college.

It varies from college to college and will be a minimum of INR 20,000.