History

To be eligible you need to have passed 10+2 or equivalent from a recognised board or you must have passed BPP with PSS from NSOU / Passed 10+2 in vocational courses from a recognised board.

Hi Zaeden,
This will depend on the university's criteria and how impressive your overall profile is. A very good SOP and LORs can help but not a guarantee. Please write to the universities before applying.

For appearing in set exam you must have 50% marks in specific subject in PG. & B.Ed. in any discipline. So, you can appear only after doing B.Ed. So, having completed your PG do B.Ed.

You need to thoroughly revise your school syllabus of 9th-12th of history.

Hi,
MA in history from BHU is a good.
As you have done your BA from DU you should try for DU first.
I would like to give you a personal opinion, as you have done your BA in history, you can option for MA in archaeology if you are interested.
The colleges to pursue archaeology are-
ICHR, New Delhi
Archaeological Survey of India, Delhi
MS university of Baroda
Mumbai University
University of Madras, Department of Indian History and Archaeology
Banaras Hindu University