M.A

Hi Sravz,
Yes, you are eligible to apply for MA in Communication in Madras Christian College. You need to have secured at least 50% marks in your graduation. The selection process is done with a written exam called Tamil Nadu Common Entrance Test (TANCET). It generally has 4 sections like any other entrance exam including Quantitative aptitude test, Reasoning ability test, English language test and General Knowledge.

If you are thinking of doing correspondence course then IGNOU is the best university for it because it's very highly reputed and in fact its worlds largest open university.
But a regular course is always a better option than a correspondence course.

Yes St. Joseph College offer the above-mentioned course.
Link: http://www.sjc.ac.in/courses.html.

Yes, you can pursue 2 degrees simultaneously. The University Grants Commission (UGC) has finally given the go-ahead to students to pursue two-degree courses simultaneously.

Yes, you can. But confirm it once if the Kerela government is conducting any such exam or not.

MBA in media is a better option.

I would suggest you to opt for MA ECO, as it will have immense scope as far as job opportunities are concerned.