VFX

You can go for Animation course. Drawing is always something that has been closely related to animation.

Yes, you can. A Diploma course is considered equivalent to 12th. So, you will be deemed eligible.

Yes, there are some colleges, which provide you this course on the basis of class 10th and you have to show the gap certificate and class10th migration certificate.

It is really tough to directly comment on any institute best or not or answer which is the best institute in a city or country, especially in India for domains like web designing, animation and VFX/editing/post-production or gaming, etc., where many institutes offer many types of courses for different duration for almost all the same pipeline. We need to see the content of the course, duration, cost, infra, earlier students outputs and skill developed, in-time course completion record, certification process & delivery of the certificate in time, etc.

As the fees is not disclosed by the college authorities. I would request you to contact the college officials.
Link: http://www.frameboxx.in/~framebox/animation-school/frameboxx-animation-schools-in-india.php

These days there are a lot of freely available resources to get you started. I think what you could start with is a bit of reading since VFX is such a wide field and identify what interests you most. Otherwise, you could start with learning 3D modelling and texturing, rigging and animation, effects, and compositing like a generalist. I think the key really is identifying what you really want to do in VFX and focusing on that. There is obviously no harm in knowing a bit about all aspects (employers prefer that for sure), but mostly there should be a singular area of focus.