IIT

The tuition fee per year for BCA in DY Patil is 55000/- INR. For more information regarding this course, kindly follow the link:
http://www.dypiu.com/bca-mobile-application-and-information-security.php

I would prefer you to thoroughly study your 11th and 12th syllabus. Prefer NCERT books for study solve their whole questions. Go for the link below to know about JEE Mains and list of books for preparation for JEE Mains:
https://www.askiitians.com/iit-jee/main/preparation-tips/

Actually, FIITJEE is better than Resonance for IIT-JEE Mains+Advanced coaching. FIITJEE is good in terms of practice papers, daily tests, doubts clarification, detail explanation, grand tests, etc.

You might have a chance if you have any reservation criteria else give it a try. You have very great chance to get into this institute with this rank.
Attend the counselling and choose your options appropriately.
Try shiksha college predictor for better analysis.

Yes, you can change the branch in second year but for that you need to top the entire batch and branch should also have a vacant seat, usually there are few seats vacant.

Go to Kotak or Indore otherwise Delhi will be good option for preparation of IIT-JEE. These cities have good atmosphere for study.

No, the criteria is of 75% marks for all students.

It depends from person to person. I personally believe that you should definitely drop for JEE. You know you are afraid that you may lower your marks, which has a very low probability of happening. But if you drop and do well next year, you could easily get a government college, which you have always wanted to and let me tell you, my friend, if you give your 100% next year, you shall get CS. You just can't let your fear stop you from trying. If now you let your fear stop you, then you are in a big trouble. Don't even think about marks, just go study.

Hello Pranjal,
Yes, of course you can easily appear in IIT-JEE exam next time to take your score to the high level. You have to only fill the improvement exam form by online mode, on the official website of CBSE. The online applications are normally out for students in the month of August or September every year.