M.Sc

There are some good universities in the country that lay a lot of emphasis on placements after the completion of the course of the students thereby providing them with good placements and placement assistance. Some even offer scholarships to meritorious students.
Many private universities offer admissions without entrance tests on basis of your marks in previous qualifying exams.
Check websites of some of the universities.
Good luck.

Yes it is possible to pursue PG along with B.ed.You are definitely eligible for UGC NET, as long as it is from a a recognised board

Yes, it is possible.

You can join R&D organisations in both Government or Private sector after M.Sc Chemistry. In addition you can join all Government services where eligibility is graduate degree. You can join Defence Services and Paramilitary forces. You can also appear for PO and Clerical services role in Public sector banks. You can also do MBA to change stream.

Praveen, Delhi University would be appropriate. For the latest changes in fee structure I suggest you personally contact the university.