Uttar Pradesh

I think you should choose Seemant Institute of Technology because LU doesn't have any good placement record and B.Tech is a newly launched course in Lucknow University.

SRGI, SRMU, IET and Bansal are the best colleges in term of placements.

Yes, of course, you can get admission.

Yes, you are eligible to take LEET.

GLA, Mathura is better than ASM because GLA has a good placement record and also GLA has good faculty members.

Here are some institutes:
Institute of Engineering and Technology, Lucknow
Madan Mohan Malaviya University of Technology, Gorakhpur
Kamla Nehru Institute of Technology, Sultanpur
Bundelkhand Institute of Engineering and Technology, Jhansi
University Institute of Engineering and Technology CSJMU, Kanpur
Dr. Ambedkar Institute of Technology for Handicapped, Kanpur
Nitra Technical Campus, Ghaziabad
Feroze Gandhi Institute of Engineering and Technology, Raebareli
Government Engineering College, Banda.

No chance, you should also think about other college options. But keep an eye on the counselling process, maybe in last round.
Good luck.