Computer Science and Engineering

Yes, you can get Government College with CS. As, I see your rank is too good, you are eligible to apply. Go for counselling and confirm your admission.

Admission in HBTU is done via JEE Mains.

It depends upon your course/branch.
Like, if you are getting chemical in Thapar University and ECE/CS in Jaypee, then you should go with Jaypee.
Branch matters more than college.
Both are private universities.
If you want to pursue same course, then go for Thapar University.
Thapar University has good pl

You have less chances for CS but you can take IT branch in GL Bajaj.

Depends on your rank in JEE Mains. Check this link for cut-offs in NIT-K (Surathkal):
https://www.shiksha.com/college/national-institute-of-technology-surathkal-mangalore-24187/admission#admission

CET rank doesn't matter for NIT-K admission. Only JEE Mains rank matters.
Check the below link for cut-offs:
https://www.shiksha.com/college/national-institute-of-technology-surathkal-mangalore-24187/admission#admission

If you want to learn coding in depth, then sorry, NDA doesn't provide you with that option because in NDA, the main focus is to prepare you as an officer.

https://www.shiksha.com/b-tech/resources/upsee-college-predictor
Use the college predictor link which I am sharing here to know about the college you can get.
Good luck.

https://www.shiksha.com/b-tech/resources/upsee-college-predictor
Use the college predictor link I am sharing here to know about the colleges you can get.
Good luck.

If you fall under general category, then it is tough, but for other categories you might stand a chance.