Game Design and Development

Anil, you can opt any stream but it will be good for you if you opt computer Science as one of the subjects in 11th.

Find the eligibility criteria here:
https://www.icat.ac.in/admission-eligibility.asp

Yes.
If commerce students are interested in game designing, they can apply for that.

Here is the list of some top affordable colleges for game design in India. NID (National Institute of Design), Ahmedabad. IDC, IIT Bombay. Pearl Academy, (Delhi, Mumbai, Jaipur)
NIFT, Delhi. MAEER'S MIT Institute of Design, Pune. Srishti School of Art Design and Technology, (Bengaluru, Pune, Trivandrum)
Indian School of Design and Innovation, (Mumbai)
If you want more, then just visit: https://www.shiksha.com/it-software/game-design/colleges/colleges-india.

Yes, it is a good choice, there are many demands of game design developer in market, not only in India but abroad too. If you are doing Diploma in game design, then you can get a good job, or do freelance, but if you want to grow more than I would suggest you to do Masters in game design. Most of abroad companies require Master's degree for providing you jobs.

Yes, you can get in to FX School.

Yes, according to eligibility it is mandatory however you can call up the admission dept for more info
https://www.shiksha.com/it-software/game-design/course/bca-in-game-development-seamedu-school-of-pro-expressionism-pune-balewadi-231149

To get complete list please follow given link
https://www.shiksha.com/design/communication-design/colleges/game-design-colleges-Jaipur.