M.A

Dear Sandipan Kundu,
If you want to settle down, go for MBA. If it is from an international university, it would be great to pursue MA philosophy. Check out your settlement after some time.
All the best.

Yes, it is possible. You need to be brilliant academically. You should appear for IELTS exam.
For more details visit the website of LSE.

To get an exact answer, please clarify your question.

Since you are pursuing your MA in psychology from IGNOU, check up with the university guidelines. Also, since psychology is a practical subject, you will need hands on experience. Do apply for internship at a reputed institution and dedicate a good amount of hours to it.
I hope this answer helps.

Yes, private institutions can give admission to those who had graduated at 40% -50%.
Go for it.