Engineer exams

Different engineering entrance exam has different eligibility criterion. It will be difficult to advice unless you specify your exact requirement . You may look at https://www.shiksha.com/engineering/exam for details of all engineering entrance examination options and their details.

Syllabus of IIT JEE and BITS is same but in BITS you have to prepare for English. Also, the level of BITS is higher than that of JEE Mains and 12th board but low in comparison to JEE Advanced. I think you should first focus on JEE Advanced so can you will be able to solve good quality questions and able to clear both BITS as well as JEE Advanced
Best of luck.

You may refer to following link for information of all engineering entrance examinations: https://www.shiksha.com/engineering/exam

Of course, you can crack diploma in engineering entrance exam after class 10th. Bharat Bharti book would be best for you.

If you are not confident enough about qualifying JEE Mains, then drop a year. Study hard, solve mock test papers and strengthen your weaknesses.

NDA entrance exam is a key to enter Indian Army at recognised posts.If you are interested in engineering you may also try Indian Navy, Indian Airforce.entrance exam for Marine and Aeronautical engineering. Indian Army also recruits from top enginnering colleges like IITs or NITs.but better you give NDA

I think it is possible.however I will suggest you to visit upsc.gov.in for detailed information.