M.Phil

Yes, you can pursue the same from here. They provide this course. Good luck.

But, please, check beforehand. The UGC in the recent times have changed their regulations. Ph.D. has come to occupy an important place. A part - time pursuit is not allowed, these days. But, still, you can get a solution, after you get an admission. You can talk to the Head and seek his consent.

Yes, the courses are UGC approved.

I am not sure M.Phil exists anymore, as the UGC doesn't approve of it, anymore. You have to go in for Ph.D. You may have to publish a couple of papers, before applying for Research. English Literature is offered all over India and there is no problem, on that count. The spade work must be completed,

M.Phil should be pursued through Regular (Full-Time 1 year/ Part-time 2 years) Mode only.

You can see all the relevant details about the exam on this link-https://www.shiksha.com/university/cochin-university-of-science-and-technology/cusat-dat-exam.

Yes, there are many colleges. Some of them are U P Rajarshi Tandon Open University (UPRTOU), Wisdom School of Management, and Greater Noida.