Animation

There is no stream constraint only your interest matters.Therefore you can go for graphic design course after B.Sc IT.

To know about the exact fee structure request you to directly contact the institute: http://www.zica.org/contact-us.html

Following are the best options for you:
Asian Institute of Gaming and Animation
Arena Animation
Animaster Academy

No good college will give you admission on the basis of class 10th. I would suggest you complete class 12th and then start seeking admission in a college.

You can see the link for details:
https://www.shiksha.com/university/dev-sanskriti-vishwavidyalaya-haridwar-314

For taking admission in 2018 all you need is to have is HSC or equivalent from a recognized board.

It is a bit tough to directly comment on any institute. Before deciding on any institute, it would be better to check content of the course, duration, fee, infrastructure and faculty.
Arena Animation is one of the best, as it offers highly focused course high-end Animation Training with specialization in 3D Animation.

NID entrance exam basically seeks to assess your traits such as creativity, perception, abstract thinking, spacial ability, and the basic level of GK. All of which are essential ingredients for pursuing this program.
Please refer to below links for better understanding: https://www.shiksha.com/design/industrial-product-design/articles/nid-entrance-exam-2016-last-minute-tips-important-documents-to-carry-for-dat-blogId-11944 and https://www.shiksha.com/articles/how-to-clear-nid-dat-tips-from-shortlisted-candidate-blogId-12190.