Lucknow

Yes, according to your rank, you can easily get admission in IET, Lucknow. In CS, there is a lot of scope like you can become a game developer, programmer. etc.
Do visit the official website of IET, Lucknow for further updates about the admission. Do upvote if the answer is helpful.

Before applying, you must go through the best colleges in Lucknow for event management like Integrity Institute of Management Technology, Leo Edunomics, Aurous Institute of Management and many more. As each and every institute has there own set of criteria for admission process.

Check out this link:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

Yes, you can apply for BA Hons in economics in Lucknow University.
The eligibility criteria for this course is 10+2 with minimum 60% and admission is based on the score obtained in the entrance test conducted by the university with the academic performance.

Yes, you can get admission in IET at this rank. All the best.

Please refer to the link provided below for details regarding eligibility, admission process, fee structure for this course from BBDU, Lucknow. https://www.shiksha.com/b-tech/course/b-tech-in-electronics-and-communication-engineering-babu-banarasi-das-university-lucknow-205184.

I'm not sure of any other government college but IET Lucknow is not possible for you with this rank. They only have 500 seats.

Here is the seat matrix for IET Lucknow. You can get admission here:
Chemical Engineering 60
Civil Engineering 60
Computer Science and Engineering 60
Electrical Engineering 60
Electronics and Communication Engineering 60
Electronics and Instrumentation Engineering 60
Information Technology 60
Mechanical Engineering 60

LUCKNOW UNIVERSITY is very good for pursuing MBA if you get admission in LUMBA which is there only in the old campus.

No. Look for other colleges like LUCKNOW UNIVERSITY or Amity or BBDU.