M.A

According to me yes, you can go for MA in psychology, but it would be very hard target to achieve you will have to work very hard.

age limit not more than 21 years

Yes, this course is available, but Umair you should go for a regular course, reason being, a part-time course will merely help you in getting a degree or Diploma but for practical and hands-on experience, you should join a regular course. The best fashion designing colleges are:
National Institute of Fashion Technology (NIFT)
National Institute of Design (NID)
Lovely Professional University (LPU)
National Institute of Interior and Fashion Technology
Pearl Academy
Institute of Apparel Management
International School of Design
Indian Institute of Fashion Technology
LISAA School of Design
Vogart Institute of Design and Management, Delhi.

Kindly visit this link:
https://www.shiksha.com/mass-communication-media/journalism/course/m-a-in-convergent-journalism-a-j-k-mass-communication-research-centre-okhla-delhi-7797

yes, you can apply for the course part time or you can do the same in distance education.
good luck

Hi Mansi, Amity University is a very good university in the private category. Their advertising and PR course in M.A is really good and be sure you'll get good campus placement.
Best of luck.

Yes, if you know some telugu then you can pursue MA telugu. Good luck.