Science

Whichever you have interest and aptitude in !
Both are niche fields, with less number of professionals and less number of jobs. You would need to specialize to remain relevant.

Yes, some universities like LPU do offer the PG programme where the eligibility is flexible to let the graduates from related fields get into.

Yes, you can take, provided you qualify the eligibility criteria and cut off of your preferred college.

You need to be in class12th with the medical stream.

If you have passed B.Sc. Agri, and didnt get any campus placement, I suggest you to go in for post graduation in your strong area, this is distressed time in economy, getting a job won't be easy, meanwhile you can apply for government positions whichever come by.

Yes, you can, but check the eligibility and cut off first.

Yes, some private universities will be providing this programme.