M.A

After completing B.Sc in Zoology, you can look for M.Sc in Zoology/Applied Zoology. You can also try for courses in diverse areas like software or management. MCA degree is a good option for B.Sc students. If you have a flair for management, look for MBA or PGDM program. Short term courses in software offered by institutes like GNIIT or Oracle will be useful.

Few steps to start GATE preparation:-
1. Know your GATE exam syllabus
2. Select Best Reference Books
3. Prepare a study plan
4. Prepare own Preparation Notes
5. Practice Previous Question Papers
6. Practice few Mock Test Papers

Yes, you are eligible to take admission in B.Ed in the same university but not in the same year. After the completion of your Masters, you can apply for B.Ed. At a time, you cannot apply for two different courses either in the same university or different universities.