CBSE 10th

It depends on the school. Different schools have different criteria depend on the number of students and infrastructure available.

Please go through this article about commercial pilot training for your answer
https://www.shiksha.com/career-in-commercial-flying-all-you-need-to-know-article-13472-1

First of all a very warm congratulations to you for scoring so good.Now coming back to your question, you are eligible to take admission in any reputed institute of the country which has a cut off list of such percentile.Also you have done your bachelor's in mechanical so there is a good scope for you to get a good institution a bright future is waiting. All the best for future.

Yes of course you have a good profile and you are eligible to apply as long as you have good MAT or CAT score as well.

Yes they help a lot. Especially you need to have a 50% or more in graduation.

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

Computer science will help you to get the basics of C/C+. It includes flow chart, programming skills like loops. These are important aspects of various engineering fields. You will come across simple algorithms during your work in any industry and basic knowledge of algorithm and flow chart preparation will come handy.
Even a simple IF function in excel uses simple knowledge of C/C+. You can also look at curriculum of any engineering course 1st and 2nd term. Do have basics of JAVA and C/C+ irrespective of your stream of specialization.

Most of the IIM's have a criterion of more than 60%. Still, you can try as a lot depends on your personal interview as well if you are shortlisted.

This is the first time that MBA-HRM programme in XIMB-XUB is accepting NMAT scores. So we are not sure what can the cut off mark be. Give it a try! Your other academic credentials seem very good.