Trichy

I dont think there is any chance of nit & iit based on jee advance so u r not elligible for iit

IIIT's take admission as per the JEE result and normalized +2 score . But one needs to apply separately on their admission notifications. Admission is based on all India Rank. state ranks are not considered for admission usually.

There is no point giving a false hope. I would suggest start looking for admission in premier private universities like BITS, MU and Lovely Professional University etc.
Taking a drop would not be a logical step as gap year affects your career a lot.
Dont worry on the placement or Education part. If you would be good you would obviously do well. Best of Luck.

plz check below colleges in tamil nadu.Cannot be so specific for already niche course so check for colleges i tamilnadu.
https://www.shiksha.com/mba/colleges/mba-in-aviation-colleges-in-tamil-nadu

You have very good chances

You have a very good chance of getting CSE in NIT Trichy

I would suggest NIT Trichy because of the facilities it provides for students of the CSE department. It offers several research and funding facilities and has labs for student use without restrictions. Professors here are knowledgeable too and can help you.