Gujarat

Hello,
Kindly visit the following link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjPs-iFqpTcAhWMRY8KHariB-kQFjAAegQIBBAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H.

In some universities only NEET Score is the eligibility criteria. And, based on your score whatever it is, they decided a merit list for selection in their Colleges. You can try for paid management seat in Top Deemed Colleges for B.A. M. S. In Maharashtra Karnataka and Rajasthan also.

No, ITM Universe, Vadodara and ITM University, Gwalior are different. Please check out the links below for details :
https://www.shiksha.com/college/itm-universe-Vadodara-36486
https://www.shiksha.com/university/itm-university-Gwalior-36449.

You can get the detailed list of last year's CMAT cut-offs for all the universities and colleges here:
www.jacpcldce.ac.in/mba.asp

I think you better to join in top ranked colleges.

Refer the following link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/resources/college-comparison&ved=2ahUKEwiosLmEmI3cAhXMq48KHR4yAb0QFjAAegQIAhAB&usg=AOvVaw3y5SpvbIBeIOXTZhH2ugyJ

Yes, you can definitely apply for admission in MSU, Vadodara for B.Sc (honors) in food and nutrition.
78% in PCB in HSC is more than enough for you to apply. State board is always great as it helps to get admission in any university. Apply soon.

Depends on which branch you have opted.