B.Tech in Lucknow

Frankly speaking, IIITs are well known for information technology courses. It's quite tough to differentiate between these institutions. However, to help you I am attaching a link that will give you all the required information about not only these institutions but all the colleges in India which are offering this branch for studies.
https://www.shiksha.com/b-tech/ranking/top-computer-science-engineering-colleges-in-india/46-2-0-0-0
Best wishes to you.

Minimum rank is needed to qualify the Lucknow University exam.

No, Babu Banarasi Das Northern India Institute of Technology (BBDNIIT) college is not a government college, this college totally private and hence the fees of this college is too high.

Yes, it is a good choice as this college as tie-ups with some foreign universities that offer student exchange programme in summer that provide many opportunities to the top performers in the academics.

Your rank is little bit high. That's why, you can't get the Lucknow University. You can get a seat in Galgotia College of engineering and technology in electrical and electronics engineering branch, ABES engineering college in ghaziabad etc. I am giving you the link please check it once. https://www.shiksha.com/b-tech/resources/upsee-college-predictor?utm_source=shiksha&utm_medium=email&utm_campaign=clientmailers
I hope your query is resolved.

Institute of Engineering and Technology, Lucknow Central Institute of Plastics Engineering and Technology, Lucknow.

Hi,
Shri Ramswaroop Memorial College of Engineering, Lucknow has an overall ranking of 5.9 and and stands 7th in ranking, so of course, it's a good option to pursue B.Tech in CSE but BBDU, Lucknow stands 1st with an overall ranking of 6.7.

Hi,
Kindly use this popular college comparison tool by Shiksha to compare these colleges:
https://www.shiksha.com/resources/college-comparison

As the result of compartment exam came late so you have to contact to your target college that what are the process of getting admission after my compartment exams result generally many college take some money as a security that you should pass the exam and take admission in the college so you should contact to college.