Game design

Hi,
There is a list below of institutes who provide Game design and development:
https://www.shiksha.com/search/?q=Game+Design&sb[]=43&sa=1^0^0^0^0^43^0^0^0^0^0^0^0^0^sb:43&rf=searchwidget&ct[]=1
In India, there are plenty good institutes are available in Game design and development. I would advise to take a course from India join somewhere. Over the years, after have experience then you may move to abroad if more options are there.

Hi,
You may refer to the following link:
https://www.shiksha.com/search/?q=MCA&bc[]=103&sa=278^0^103^0^0^0^0^0^0^0^0^0^0^bc:103&ts=14925986&rf=searchwidget&ct[]=278

You can do a Diploma in Gaming.

Hi,
You may pursue this course along with your graduation. A degree with game designing skill will help you to get a better job. However, graduation is not mandatory for any game designing course.

Yes, you're eligible. You also require creativity skills. Knowledge of programming languages can be an added advantage. You can pursue Bachelor's degree or a certificate course in animation for game design.

Only through self learning and practice, you can become a game designer in India as most of the courses that are available either teaches you how to become a game artist or game programmer but never a game designer, even the courses that says Game Design on its title, focuses heavily on game art side of things and little on game design.
Game design is a vast subject so my suggestion to you would be to read books or watch tutorials on game design, play games not to enjoy but to deconstruct and understand them and most importantly try making some games yourself.

Hello Vipin,
These days a large number of engineers are unemployed. Hence it's essential that one must think of those courses which will give better chances of employment. I feel that B.Sc with computers and game designing or web designing will get you job. Go ahead.