Engineering

Yes, you may have some chance to get the mechanical branch in this college. I am not sure about that but you might get it because your rank is not so bad.

Yes, it is possible. You can start your Polytechnic Diploma with the desired branch after which you can do your graduation also.
All the best.
Good luck.

You can get admission with your marks through counseling.

Yes, you can sit for the aptitude test. You should fulfil all other criteria for the exam. Go to the official website of IISER and kindly look over it.
All the best.

You can get KIET, BIET and CSJMU.

At 3600 rank, you can get admission in KIET, KNIT, BIET, CSJMU, MJPRU and Galgotias.

You should decide for yourself. If you are confident that you can crack the JEE for CSE then you should drop a year, otherwise, don't waste your time. You can also lose what you have now. So, as per my opinion, don't drop and start studying now in IIIT. Placements totally depend on you. If you have

Well, both are top NITs but you should go as per your interest. MNIT, Jaipur is among top 5 but civil branch has less scope as compared to EC branch. You should go for EC branch which is most demanded and future scoring branch. All the best.