Game design

You may learn game designing for free from eDX or Udemy.

You may do the course from the below link:
https://www.edx.org/course/introduction-game-design-mitx-11-126x-0
You may also refer to websites like coursera and udemy for the same.

Refer to the linke below:
https://animation.shiksha.com/game-development-courses-in-pune-categorypage-12-94-1-0-0-174-114-2-0-none-1-0

This has nothing to do with being a girl or a boy. You must be good at animation tools, imagination, and some high level programming as this is a part of this course.

Friend, Gaming is a less touched area hence interest and expertise can do great good in no time. Other than that, cloud computing and architecture is a great choice looking at the trend today. Prefer web after cloud computing. Computer science is a skill and hence don't worry about college and other things. Just get any best college you get and go ahead. Most of them have nothing to give other than degree.

No, because commerce is related to accountancy, marketing, business, etc. which relates to commercial elements and game designing is based on software and graphics, so I don't think by choosing commerce you can do game design because for this you need to do different courses based on game design.