Zoology

No, it's not. The subject in which admission is sought must be an Honours subject. In B.Sc (Hons) a subject is studied in all the three years at graduate level.

You must have Chemistry as one of the subjects at the UG level and Zoology must be your Honours subject. At B.Sc. (Hons) level, a subject is studied in all the three years in UG.

After B.Sc, it would be difficult to go abroad for studies, you need to complete Master's degree (at least).

Yes, you most definitely can. Admission into M.Sc zoology would also depend on how you perform in your undergraduate degree, as eligibility into universities may be based on your results in your UG program.