Distance/Correspondence

No, there is no such options.

Yes, of course, you can do MBA as this will help you in getting more information about what you want to pursue. This will also help you in understanding the base and all the systematic approaches and functions for how you'll manage the things.
All the best.

I think you should go for the distant learning colleges available in Pondicherry itself instead of finding any other university which has a study center here. In Pondicherry, 2 colleges provide master's through distant learning. Follow the link given below to get details about both the colleges
https://www.shiksha.com/humanities-social-sciences/psychology/colleges/colleges-Pondicherry

Hi,
Yes, you can apply for M.Sc (physics) in correspondence, as in most of the distance colleges the enrollment is open now. Hope you got your answer.

Please refer to the link given above to understand what all is required to get admission in this course.
https://www.shiksha.com/humanities-social-sciences/languages/course/m-a-in-sanskrit-savitribai-phule-pune-university-ganeshkhind-274469

There are plenty of colleges available near Pondicherry for distant learning in psychology. In my opinion, Annamalai University is the best for distant learning. It is a famous university and the best part I like about them is that they call you to live in their university for a month or so for all the practicals and research which no other university provides. Some other universities are:
1. Distant Education College
2. K. S. Memorial education trust
3. Cooperation College for Education.