Colleges in Kolkata

It's totally entrance based exam. You should check their official website for it and cut off too.

Get the list of colleges for Bachelor of Hotel Management BHM in Kolkata. Click here:
https://www.shiksha.com/business-management-studies/colleges/colleges-india?rf=filters&bc[]=37&st[]=127&uaf[]=city&uaf[]=state.

As of the latest information, Presidency University accepts the admission form of students who have passed 10+2 in 2022 and got at least 65% in the best 5 subjects in 12th.

You will not get CSE but you may get IT if you participate in spot round ( chances are also very low).

If you are from West Bengal, then you will definitely get admission in Jadavpur University, but you will get lower branches. For other state students, it's very much difficult to get admission in this rank but you may wait till spot round.

Yes, you can get admission through lateral entry.

For admission firstly you have to appear in WBJEE Exam and have to get good rank .
After that you need to register for WBJEE Counseling and you will get seat ( if rank is good ).
Jadavpur University also organise spot round whose notification you will get in College Official website.

Yes, you can get admission through lateral entry.

There is no direct admission in Jadavpur University for Engineering. For admission in Jadavpur University you have to appear in WBJEE Exam. If you have a domicile Certificate of West Bengal then you can get admission even at some lower rank.