UPCAT

There is a possibility that you can get admission through the JEE (Main) rank or you can try for admission by applying on colleges websites and fulfilling the eligibility criteria for vacant or left seats.

No, if you have been locked your choices, probably, you will not be able to do it again.

Fee wavier seat is not considered in lateral entry.

Only in 1st and 2nd round of counseling your BC rank will be considered. After that your general rank will be considered.

You can go for BIET Jhansi, IERT Allahabad or REC band.

You have a good chance for LU.

There is no chance in BIET. You may get REC college and government universities if you have filled choice and locked during counselling.

Yes, absolutely. According to as per AICTE norms and UPTU/AKTU/GBTU all the engineering colleges and institutions have to fill some of their seats for lateral entry. All the branches have almost 12 seats for lateral entry, especially talking about government. Engineering colleges in UPTU it is available in all colleges/institutions. To get more details check it here with section 2.2:
https://aktu.ac.in/pdf/about-us/

Either you didn't submit the fees for counseling or there might be some document error. I suggest to consult with UPTU Authorities, or
You should visit IET, Lucknow.

Yes, you may get government colleges of UPTU easily. Yes, absolutely. According to as per AICTE norms and UPTU/AKTU/GBTU all the engineering colleges and institutions have to fill some of their seats for lateral entry. All the branches have almost 12 seats for lateral entry, especially talking about the government. Engineering colleges in UPTU it is available in all colleges/institutions. To get more details check it here with section 2.2:
https://aktu.ac.in/pdf/about-us/