Engineering

Yes, it is necessary for UPSEE document verification and admission.

I would suggest you to visit josaa.nic.in
Here you would get to know all about the counselling procedure, important dates and document required.

Engage Publication is for JEE Mains level and other equivalent examinations. Do not rely on either of the books for examinations like JEE Advance. For Advance level you can refer ML Khanna. Its question bank is very good. Refer IIT mathematics by Das Gupta. It is the most important book recommended

Use COMEDK college predictor for predicting the colleges you can get based on your rank. Link is given below:
https://www.shiksha.com/b-tech/resources/comedk-college-predictor

Since you won't get top NIT's through Mains rank, it's better to go for IITs. Since IIT is a brand, you will have more options in IITs and only in top NITs. Since you won't get top NITs, it's better to opt any IIT.

In Coimbatore there are 2 top colleges - PSG and Amrita. Whereas in Chennai SRM, Satyabhama and VIT are top colleges.

Chandigarh University
Lovely Professional University
Amity University
These are the best colleges for aerospace engineering except IITs.