India

Yes. You can get the list of college by given link
https://www.shiksha.com/hospitality-travel/event-management/colleges/colleges-Delhi-ncr.

For ST category, last year cutoff were around 89%, so if you just reach that cutoff, you can easily get admission. Along with these, practice well for GD/PI.

Considering your profile, good Acads and background diversity, if you score good in CAT and in GD&PI, you can easily get admission.

You can seek admission through any mode on the basis of a single application form, subject to fulfilment of eligibility criteria. Mode 1 70% seats on the basis of JEE (Main)-2019/NEET-2019 rankings
Mode 2 30% seats on the basis of 10+2 PCM/PCB scores
For more details please checkhttps://admissions.thapar.edu/online-application-form.php?_ga=2.61410220.1049489634.1552475651-109155482.1542883253
Their applications are open. Hope check it out.

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, below is the list of some colleges offering M.Tech in Automobile engineering in Maharashtra, Symbiosis Skills and Open University, Pune
Dhole Patil College of Engineering, Pune
Dr. D. Y. Patil School of Engineering and Technology (DYPSOET), Pune
Shastri Group of Institutes, Pune
School of Engineering, Ajeenkya DY Patil University, Pune
If you want more, just visit: https://www.shiksha.com/engineering/colleges/m-tech-automobile-engineering-colleges-pune.

If you are looking for best colleges in Maharashtra to pursue M.Tech in automobile engineering, then I can provide you some list as below. Symbiosis Skills and Open University, Pune
Dhole Patil College of Engineering, Pune
Dr. D. Y. Patil School of Engineering and Technology (DYPSOET), Pune
Shastri Group of Institutes, Pune
School of Engineering, Ajeenkya DY Patil University, Pune
Apart from it, if you want more list just visit: https://www.shiksha.com/engineering/colleges/m-tech-automobile-engineering-colleges-pune.

There are lots of colleges in Rajasthan offering automobile engineering. Below is the list of some top engineering colleges for automobile engineering:BITS Pillani
MNIT Jaipur
MBM Jodhpur
CTE Udaipur
LNM Institute of Information Technology, Jaipur.