B.Sc

What is the total no of seats and do you have any reservation?

Please go to the given below that will help you in predicting all possible colleges you get through this rank
https://www.shiksha.com/b-tech/resources/mhcet-college-predictor.

List of best coaching institutions for IIT JAM biotechnology Preparation in Delhi:
Career Endeavour
Aakash Institute (Medical Wing) - NEET
Indian Institute of Technology
KapMan Life Science Academy
IIT - JAM/ Biotech/M.Sc Coaching
DIPS Academy IIT JAM Mathematics Coaching
IIT jam statistics coaching in Delhi
IIT Jam Coaching Institute Delhi - Path Finder Classes.

The total fee for Integrated M.Sc courses at BIT Mesra for 2019 batch is 815000. An additional amount of Rs. 25,000 is required to be paid at the time of admission. This includes Rs. 10,000 caution money, which is refundable. Please note that the total fee does not include mess charges.
For total fee break up of this course and other courses, please visit this link https://bitmesra.ac.in/UploadedDocuments/admadmission/files/Fee Structure 2019 Batch (Final) - 25 Jan 2019.pdf

I cannot understand about which university or college you are asking for doing BMS via correspondence. Please mention the institute.

Kindly visit this link:
https://www.shiksha.com/university/lucknow-university-lu-21456/admission

Yes, you can take the admission in this course. The eligibility criteria for this course is pass in 10+2.

Yes, with 51.38%, you will get admission for B.Sc in Biotechnology. You can try for it.