ICAT Design and Media College, Chennai

There is a college named Backstagepass institute of gaming and technology, they offer Game Art and Design & Game Development, Course of 4 years each. And the fee structure is INR 1.4 lakhs per year in both of the courses. If you want a future in gaming, this is the best one as far as I came across.

The fees for mechanical diploma for 3-4 year course is 60000 to 1 lakh. If you are getting a government college or if you have a private college then it should be more.

If you are a student of BE mechanical then you can do game design and development after completing your under graduation.

You must have atleast 55% marks in your 12th for the entrance purpose in any undergrad course.

You read this article it may help you.
https://www.shiksha.com/design/fashion-designing-chp

Yes, of course, you can do that. Game programming requires your skills of Game Development, not the stream from which you were.
Hope a bright future ahead for you.

The general procedure is 1. Send application. 2. Wait for aptitude test intimation. 3. Submit a portfolio. 4. If selected in aptitude test, wait for the interview. 5. If all the stages are successfully completed, you will get admission.
Good luck

The fee structure of ICAT design and Media College is INR 2 lacs.
Good luck.