Anthropology

University of Allahabad does not offer B.Sc. Anthropology course.

Universities and colleges generally award Masters of Arts in fields like Languages, History, Geography, Philosophy, Fine Arts, but also Social Sciences, where they overlap with Masters of Science. This means that one subject can be offered either as an M.A. or an M.Sc.

Yes, you are eligible for M.Sc Psychology after completing B.A Psychology. Since, you have completed a bachelor degree with Psychology specialization, you are eligible for M.Sc psychology course.

You can take admission in M.Phil social work after you complete your Ph.D. in Anthropology. Simultaneous courses are not allowed.

Yes, you can pursue. There are many colleges in India which offer MA and also M.Sc in Anthropology wherein one can pursue Masters in Anthropology having graduated from a recognised university in any stream. However, there are also few colleges which ask for graduation with Anthropology as a subject

IGNOU could be a good choice. It is easily accessible and has plenty of regional centers across India. And, it is very affordably.