Bangalore

Yes, there are really good chances for getting electronics and communication engineering at Amrita University, Bangalore campus. You may not get the other campuses like Coimbatore but surely you can get in Bangalore campus.
You have a good rank which is good enough to get ECE at Amrita.

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

RBVRR Women's College and St Joseph's College, Hyderabad.

It's a good college with a good placement record and I have no idea about the fee structure.

Yes, you can join IIBS-Bangalore. It is a better option as compared to other B-Schools. Both are good colleges and placement of both the colleges is 100%. IIBS's faculty is very knowledgeable. They had read and known wide areas of management subjects. There is a visible interest in them to pass on t