UPCAT

Hello Prince,
Your rank is far beyond to get any government and good private colleges, check here to know more:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

I will suggest you to try colleges in Delhi NCR or colleges like Chandigarh University and Chitkara University. These colleges will provide you a good platform from where you can build your future.

It depends upon the cutoff which varies from year to year. You just check the cutoff and merit list of different universities.
Outside UP too you can use your UPTU rank to get admission in a branch of your choice. Check with some good private universities.

No, Jaypee Institute of Information Technology does not give admission on the basis of UPSEE marks/rank. JIIT only gives admission on the basis of JEE Mains rank.

There is difference in general rank and category rank if you want to take admission with your category rank you have to seek the number of seats available in the college under your category.

All are branches are best at their place. Scope wise mechanical branch has better scope than agricultural and civil engineering.

You will get an average private college like SR engineering College, Lucknow and RR Engineering College. They give admission on the basis of your board percentage as well.

Please check the link provided in the answer for complete detail about the college:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

JSS, KIET and many other private institutions will offer CSE as per your rank.