UPCAT

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/

OSGE- Outside UP and parents are not domicile of UP.
UPGD- Outside UP and parents are domicile of UP.

At your score you can expect JSS, SRMU, SRGI, Bansal, etc.

Yes, you have 80% chances at JSS and 65% chances for KIET at this rank for MBA.

Through Shiksha college predictor you can opt for any rank category or non-category but at the time of counseling you should have proper category certificate.

Yes, you have 95% chances to get HBTU at this rank but 100% chances for IET, Lucknow.

There are only 65% chances of CSJMU for B.Pharma but at this rank surely you can get MJPRU for B.Pharma.

There are no any changes for LEET in UPTU. But at this rank you'll not get any college, neither government nor private. For LEET government colleges like IET, HBTI, MJPRU and BIET your LEET rank should be under 100 and for private colleges your rank should be around 2k.