M.A Archaeology

Yes you can do Masters in Archaeology.

Yes, it is possible. In UNOM, the eligibility criteria is: The candidate must be a graduate from a recognised college / university. You can get more information through this link:
https://www.shiksha.com/humanities-social-sciences/history/course/m-a-in-ancient-history-and-archaeology-university-of-madras-chepauk-chennai-88314

For admission in M.A. Archaeology, you need to have a Bachelor's degree in Ancient History & Archaeology or History & Archaeology or Archaeology and Museology as a major or optional subject. In case, the candidate is of CAT -I category their minimum eligibility would be 40%.

Minimum 54% score is needed to get admission in this post graduation course. But you had a very low chances to get admission in this college. Try in any private university.

Before the age of 30 years, it would be better to do EMI in archaeology, if you want it as a career. And yes, it needs a regular class, because if you are doing in correspondence, you are not going to get any knowledge about archaeology, because it's a study, where you need to be present and get to know about everything what you have been taught.