Lucknow

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.

BBD will give you a better exposure during the course but I would suggest you to research about the placement facility of both the colleges and choose accordingly.

Amity is a good option for law but I would suggest you to go for Amity Law School, Noida. It has a better exposure and faculty.

Lucknow is not the best place for doing BCA but it's not bad too. Some good colleges for the same are:
Lucknow University
Amity
BBD
SRMU
Modern Academy