B.Sc Zoology

Yes, Absolutely, A Graduate in any science stream (Chemistry, zoology etc.) can apply for M.Sc in Food Technology.
M.Sc in Food Technology is a 2-year postgraduate course. Food Technology is the branch of food science involving the processing, protection, preparation, selection, distribution, and utilization of sheltered, nutritious, and healthy nourishment.

You have to fill first round of counseling to be eligible for second round. If you didn't fill for first round, then you are not eligible for second round.
Good luck.

There are so many options are available like:
M.Sc Zoology
M.Sc (hons) Botany
M.Sc Botony
M.Sc Microbiology
M.Sc Biotechnology
M.Sc Bioinformatics
M.Sc (hons.) Microbiology etc.

Yes, some university offers M.Sc Oncology after B.Sc Zoloogy. So, try to search the universities who offers the course.

You can pursue M.Sc (Zoology) and clear SLET/ NET for getting qualified as a Lecturer in Colleges/ Universities, else move into Ph.D (Zoology) for Research.

Being a B.Sc (Hons) (Zoology), you can pursue a M.Sc (Zoology), M.Sc (Bio-Technology), M.Sc (BioInfomatics), M.Sc (Forensic Science), MBA , etc.

Top college for B.Sc. (geology) are:
1) AKI's Poona College of Arts, Science and Commerce
2Dr. Babasaheb Ambedkar Marathwada University - BAMU
3) Fergusson College
4) Gangamai Education Trust's Arts, Commerce and Science College

You have to get deep knowledge to clear this exam and command in subject read good reference books for study. Good luck.

Which college are you seeking admission in?

No, there is no such entrance exam for B.Sc. Zoology. The admission criteria is based on marks of 10+2 and for that, the minimum eligibility is 55%.