State College

You can try for NFSC College.

Kindly go with College predictor tool which helps you get information regarding the eligible colleges:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

Hello Nikhil, I think there is a good chance of you getting admission in your state based on percentile that you have got in JEE Mains. I'm assuming that your state gives admissions in engineering colleges based on JEE Mains exam. Still I request you to attend the counselling session as it gives you a greater chance of getting admission. Good Luck.

Yes, you can enroll for the same counseling. You are eligible for the same.
Good luck.

Check the past year cutoff scores for the respective colleges under All India quota.

Here I will suggest you firstly to visit on Shiksha's college predictor:
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.

Hello,
I hope you are doing well. It depends through which category you want counselling to be done for you. If you want with general category then put the general rank and if you want with category rank then put the category rank. I will prefer you to go with category rank this will increase your chances for good college.