IIT

You can apply for the New IITs or you can apply for the NITs.

You should complete your class 12th, because the syllabus of JEE Mains is the syllabus of plus two. It will help you to get in a NIT or IIT.

You have a good rank you can get one of the best IITs with this. For the relevant information, you can visit this link:
https://www.shiksha.com/science/articles/colleges-accepting-iit-jam-scores-ranks-for-admission-blogId-13971

IIT-B and IIT-D are the best colleges to pursue CSE.

You have to take JEE Mains exam, according to the ranking only seats announce.

No, it's not necessary to pursue B.Sc Computer Science from an IIT. Check out the link below for top B.Sc Computer Science colleges in India:
https://www.shiksha.com/science/articles/top-10-bsc-msc-colleges-in-india-blogId-13473.

According to the survey, the top IITs at Mumbai, Delhi, Chennai, Kharagpur, Roorkee, Kanpur and Guwahati had an average entry-level salary of Rs 11.1 Lacs compared with Rs 6 Lacs at the top National Institutes of Technology (NITs). For non IIT's : https://www.shiksha.com/b-tech/articles/average-sala

If you are having enough budget, then go for FIITJEE or resonance.

In IIT JAM exam, Section A have 50 marks and it carries 30 Questions. First 10 questions carries 1 mark each, while next 20 questions carries 2 marks each.