B.Tech

Hello Mohammad,
Almost every institution and states allow NRI's to seek admission in an engineering college. First you need to decide where you want to take admission. unfortunately rules and procedure is different at different college. However luckily everything is spelt out on webpage of concerned institute. I am attaching a link giving you list of top aeronautical engineering colleges. Pl go through and let me know if any help is required.
https://www.shiksha.com/b-tech/ranking/top-aeronautical-engineering-colleges-in-india/49-2-0-0-0

I do not think that universities/colleges offers B.Tech in VFX and BFA.

Yes, you can but you should have and know the reason for your immigration. It can either study, work or family. Only on truthful basis that is with proof, you will get a visa.

There are 265 universities in the UK alone that is available for mechatronics. Top ten universities to name are:
Oxford University
Cambridge University
London School of Economics
Imperial London College
St. Andrews
Durham
Loughborough
Lancaster
Warwick
University College of London

You may sit in the placement process with your class 10th and graduation marks as your aggregate score would be in the 60s. However, there is a zero-day in the placement season when 13-14 companies come to campus which does not ask for any eligibility criteria. You can seize that day my friend.

Please refer to the link provided below for eligibility, admission process, entrance exams required for B.E. in Marine Engineering from Mangalore Marine College and Technology.
https://www.shiksha.com/b-tech/course/b-e-in-marine-engineering-mangalore-marine-college-and-technology-267993

B.Tech ECE after B.Sc Physics will consume a lot of your academic curriculum duration and you will still be called as a graduate and not postgraduate, I think MBA/ PGDM will be better for you unless you are too passionate about pursuing B.Tech ECE. If you go for B.Tech ECE then definitely opt for M.Tech otherwise if you opt for MBA after B.Tech ECE then you should opt for MBA now.

Please refer to the link provided below where you should be able to download the college brochure which contains placement report for this particular institute. Alternatively, you can visit college web site which contains details regarding placements.
https://www.shiksha.com/it-software/game-design/course/b-tech-in-computer-science-and-game-development-backstage-pass-institute-of-gaming-and-technology-madhapur-hyderabad-205891
(Website:- http://www.backstagepass.co.in)
Regards.