IIT Eligibility

Yes, you are eligible you don't worry about it. You have a B.Tech degree so you can do easily this hence start preparing for GATE.

Eligibility criteria for NIT and IIT is 75% in class 12th board exams.

Please visit this link-
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/amp/jee-main-exam-pattern&ved=2ahUKEwiCx5eb3IbiAhVIuI8KHXa6BjUQFjAAegQIAhAB&usg=AOvVaw2nqB-mOziaqydu0OWItb7o&cf=1
I hope this will help you.

A valid GATE score is required to take admissions for M.Tech.

Hi,
Yes, you may get IIT-B but you have to make it confirm whether they accept backlog or not. Try to find out that information first.

Hi,
Please visit Shiksha.com's college predictor-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor. Ranks keeps on changing every year and differs from one branch to another and one college to another. If you fulfill the eligibility criteria of the specific institute, you may complete further admission formalities. For now, I would suggest you to first contact the institute officials of the shortlisted universities directly for specific eligibility criteria details.

Yes, you can give Mains 3 times and Advanced 2 times.

JEE Advanced is specifically conducted by the IITs to admit students.

Admission in IITs and NITs is only after appearing in Joint Entrance Examinations JEE conducted by IITs. You have to crack JEE Advanced for IITs and JEE Mains for NITs. There is no other exam to seek admission in these institutions for a graduate degree in engineering.

Basically, the cutoffs for JEE Advanced exam changes every year. So, just stay tuned. But almost 20 percent is needed in all the subjects.