Science

I don't think Presidency offers biological science but you need to confirm that from the administration office. As far as I know, Presidency offers B.Tech, BBA LLB, B.Com LLB and MBA.

Some reputed colleges which offer this course are:
1. Indian Institute of Technology -Bombay
2. Rajiv Gandhi Center for Biotechnology, Trivandrum
3. School of Life Sciences, University of Hyderabad
4. National Dairy Research Institute, Carnal
5. Institute of Chemical Technology, University of Mumbai
6. Department of Biochemical Engineering & Biotechnology, Indian Institute of Technology
New Delhi
7. University School of Biotechnology, Guru Govind Singh Indraprastha University.

Following are the colleges which offer this course in Punjab:
Akal University- AU
DAV University
General Shivdev Singh Diwan Gurbachan Singh Khalsa College
GNA University
Khalsa College
Mata Gujri College.

I don't think you can apply to any university if you don't complete your 12th. Please clear your backlog and try again? Still, for the complete confirmation, contact the admissions office.

Yes, it is mandatory.

Yes, it is a decent college for B.Sc Agriculture. But you can also go for some other colleges that are the top private colleges for this course situated in Dehradun, Uttarakhand.

Yes, you will definitely get admission and can do M.Sc. Nutrition. By securing 269 rank, you have confirmed your admission in a good and reputed college.