CBSE 12th

Of course, since the closing rank for CS in Presidency is 52000.

No, it's not a wise idea. Go for coaching along with your studies. Both have the same syllabus. A proper mock test will help you get a good score along with your studies.

KCET 2018 College Predictor:
Use your KCET 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of KCET 2017
Get resources & insights on colleges & courses. Regards. https://www.shiksha.com/b-tech/resources/kcet-college-predictor.

Since you have given improvement for class 12th boards, from now on, you will have to put up your improvement result certificate everywhere asked. The original will not be considered.

https://www.shiksha.com/animation/2d-3d-animation/course/integrated-b-sc-m-sc-in-multimedia-st-xavier-s-college-park-street-Kolkata-281121
This is the link, where you can see the details for integrated B.Sc+M.Sc in multimedia.

If you want to get into IITS or NITs its mandatory to take up JEE. So, I suggest you for drop and go for coaching and appear for JEE. It will help you get a good future.

Please refer to the link provided below for the complete list of all courses offered by this institute:
https://www.shiksha.com/college/anibrain-school-of-media-design-viman-nagar-pune-31912

HIT -K is an autonomous private engineering college in West Bengal. It has been ranked among top private colleges in West Bengal. HIT takes admission on the basis on WBJEE and JEE mains results. For branches, like CSE, IT, ECE, WBJEE rank should be within 7000 to 8000. For branches like mechanical, civil rank should be within 10000 to 12000. The chances are quite good for your rank. Moreover, it depends on WBJEE counseling every year. So, go through it patiently.

Yes, with the help of your JEE counselling, you can get admission there.