JEE Main

Kindly visit this link:
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjttrm95qHiAhXd8HMBHUdwD_0QFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Kindly use this link:
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjttrm95qHiAhXd8HMBHUdwD_0QFjAAegQIAxAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Yes. As you have got 97.05%ile in JEE you are competent enough and eligible enough to apply for it and to secure admission so go for it and apply.

To know which colleges you are eligible for, use the college predictor tool:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

No, It's not possible for you to get admission in any of the NITs as the seats are limited to less than 600. So, those who get AIR of less than 1400 will get seats in NITs. I suggest you to go with private institutes.

You should participate in your state engineering counselling.
Best of luck.

Kindly visit this link:
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwitsZDG0KHiAhWP6XMBHf2wDBUQFjAAegQIBBAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Considering 1,50,000 students attempted JEE Mains Paper 2, you got 99.44 percentile. So, your rank would be around 810. So, there are like more than 809 people who got more percentile than you. This is just an example for letting you know. If you know what your rank is, your rank-1 will let you know how many got more percentile than you got. With this percentile, there are high chances that you can land in any one of the NITs.

With these marks, you cannot get a very good college, but you can get any average college.
Good luck.