Hey Navneet, I started my education for that in Vancouver 9 years ago at The Art Institute of Vancouver, I looked at many institutions 9 years ago and it was the best match for me especially because most of the teachers were actively working in the games industry. I was lucky to have teachers who worked at many of the local studios in Vancouver (Slant Six, United Front Games, etc.) and I learned a lot of practical stuff. I recommend you find an institution/course where you learn from instructors who have built and released games (especially instructors who've worked in a team).
I've been out of date on education in this field for a while sadly but I do believe online education for this kind of stuff has gotten really good, I'd recommend a look at Coursera/Udacity and the usual bunch of course providers as a start at least. I'll try and ask around some of my colleagues for you to see if I can give you a better answer.
When it comes to game designers, I've seen a lot of jobs where some light knowledge of scripting was required (to tweak/modify the games with simple scripting languages) in addition to the skills you listed, they're definitely in demand but I'm honestly not sure about India. In many cases this is a field where you have to put in A LOT of hours and the pay is not that great.
I hope I was able to be of some help.
Thanks for the reply. I am looking at countries other than India for graduate courses. I am also looking for places where the jobs and the universities co-exist. will make it easier to study and work.
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