M.A

You need a Bachelor's degree to be eligible for any Masters course, regardless of subject.

First, you need to complete your Bachelor's degree

Yes, you can. For Masters from any subject, you must have graduation.

After completing graduation, you can apply for masters in Hindi

Yes, ofcourse you are eligible.

Yes you can do Masters in Archaeology.

It depends on what Bachelors degree you have, because M.Sc would mean you would become a psychiatrist and it will require a doctoral degree and knowledge of medicine. With MA you can be a counselor and psychologist and also teachers, yes M.A will easily get you into NGO and preschools as well as M.Sc will too.

You can not earn two degrees simultaneously, according to IGNOU guidelines for their students. So, never do that. Otherwise, your degrees are liable to be cancelled in future.

Yes, it is quite possible currently as per the system, you can surely pursue both the courses at the same time in the manner stated.