Game design

http://www.payscale.com/research/IN/Job=Video_Game_Designer/Salary
its there for your help

I don't think any of the NIT or IIT offers game designing course.
You have to study game designing course on your own, either with the help of internet, YouTube or by taking coaching classes.

Please refer to the links for details about the colleges and their fee structure:
https://www.shiksha.com/design/communication-design/colleges/game-design-colleges-bangalore
This list will give you an insight of the colleges offering game design and based on your idea/parameters, you can decide on the college.

You can easily get education loan. You just need to talk to the bank and the college admission department.

A Bachelor of Design (B.Des. or B.Design) degree is usually an undergraduate academic degree awarded for a course or major that generally lasts three or four years. It is an arts-centered degree that is a counterpart to the Bachelor of Fine Arts (BFA) degree.
All the best.

No, it not mandatory.The minimum eligibility required for most of these courses is 10+2 or its equivalent. For becoming a game programmer, one should have B.E/ B.Tech degree in computer engineering. Online programs are also available in game design and animation.

Dear Kaushik,
AIGA does not have a course in Game designing. Game designing is something which deals with the Psychology & balance of the game, which makes the game more related to real life. We do have a game development course, "Diploma in Game programming", which helps you create games using programming languages like C-Sharp, JavaScript in Unity Engine. Fee for Diploma in Game Programming is 2 Lakhs + tax. The duration of Game programming is 9 months. For Professional Diploma in Animation, the course duration is 1 year, the course fee is 2 Lakhs + tax.