NIT

Depending on your rank and the engineering stream you want to pursue, you might hold a chance to get admission in one of the NITs.

NIT's are some of best colleges in India. In case you cannot go for a higher rank NIT, then going for NIT Jalandhar is really good choice.

Yes, you can get admission in NIT on the basis of JEE rank only.

No, you have no chance at all. You can try for other regional government institutions.

Try till the spot round. There are chances you might get it in your home state NIT. It is quite difficult but don't take a chance. Go for it at least in your counselling.

Getting NIT with this rank seems difficult. But you must try your luck till spot round counselling because there might be a seat available in some low rank NIT. And yes do try for IIIT, you will get one with this rank.

Of course NIT's are better as they are government institutions. Thapar University and VIT Vellore are private institutions. No doubt they have a good reputation specially VIT Vellore but I would suggest to go for NIT Jalandhar.

You can try for Punjab Technical University (PTU). It has courses in aeronautics that might interest you. Moreover, the university has great reputation in case you are not eligible for IITs and NITs.

Your marks in JEE Mains are really good but you did not complete the criteria of attaining 75% in boards. Hence you are not eligible.

I, fortunately, you can enter IITs or NITs unless you crack JEE. For cracking JEE you require expertise in all three subjects i.e. Physics, Chemistry and Maths. If you can unable to get admission in these institutions now, you may try again by appearing for JAM examination conducted by IITs to seek admission in M.Sc degree course .
JAM is an admission test to Master of Science and other post-graduate science programs at the Indian Institutes of Technology, Indian Institute of Science, and other institutes.