Electrical and Electronics Engineering

Yes, you are eligible to join IIT but for that, you have to appear for B.Tech lateral entry exam and in that, you have to do really good to get an IIT.

I cannot provide the exact details of the ranks but you have to get between 1300 to 3500 to get electrical and electronics in NIT-Trichy.

Yes, you can join aeronautical engineering with Diploma with EEE.
Choose a good college and go ahead.

NIT Silchar is good for mechanical branch but take mechanical only if you have high interest in Physics. Or else, go for EE.
IIEST Shibpur is also good but for Civil and CSE.

Admissions in Loyola-ICAM College of Engineering and Technology is through TNEA counselling based on marks obtained in 10+2.
Minimum percentage in class 12th is 60%.
For details, check the link below:
https://www.shiksha.com/b-tech/course/b-e-in-electrical-and-electronics-engineering-loyola-icam-college-of-engineering-and-technology-nungambakkam-chennai-184344

Hello Dipankar,
You have obtained quite a handsome rank. I feel you will get admission in your desired college with the required branch.

See, honestly, both the departments have good professors and core companies for your placement and to add to this look at the seat allotment after the 1st round. EE department has started from 29 rank and ETC dept has started admission from 51 rank, both are impressive.
So, to sum up, choose what you like. If you like working with a breadboard, resistor, capacitor, chips, etc., choose ETC. If you like to learn about motors, machines, transformers, etc., choose EE.
Good luck.