UPCAT

You can get so many government colleges and I am listing some good colleges do check:
1-Institute of Engineering & Technology
2-Bundelkhand Institute of Engineering & Technology
3-Kamla Nehru Institute of Technology
4-Government Engineering College
5-Galgotia's College of engineering & Technology.

Yes, you can get IET and other government colleges such as IET, KNIT, Bundelkhand university, CSJMU and may be HBTI too.

I think you should choose government UPTU colleges if you have a good rank and UPTU colleges should be IET, HBTI, CSJMU and Bundelkhand University. These colleges have very good placement records and these are top engineering colleges.

Yes, 90% chances that you'll get IET Lucknow because lateral entry depends on the vacant seats in second year.

It is Rs. 20,000.

2nd July, 10th July and 17th July.

I suggest you to check out this
https://www.shiksha.com/upsee-college-predictor

Please mention what is your GN rank because counselling is done by GN rank.

Yes, you can good colleges on the basis of your SC rank
such as HBTI, IET, Bundelkhand University, MJPRU, etc.