SMEAT

Please use college predictor tool for better results
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjdmKnz4bHiAhU1jOYKHZnJDRsQFjAAegQIAhAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

For government colleges, the fees will be the same. But, for private colleges there is a different fee structure if you go through TNEA and the fees will be higher if you go via any other ways. And yes, the fee structure varies from one college to the other. Generally, government colleges have lesser fee than private colleges.

Yes, with your category you will easily get a seat here.

Yes, you can get admission in NIT Trichi. But, I can't assure you about your course. All the best.

No, it's not possible for you to get admission in any of the NITs. As the total number of seats are less than 600, those who get AIR less than 1.5k can only get seats in NITs.

Use this to know:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Kindly go through the following link: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can surely get admission there. If you have any query do let me know in the comments down below. All the best.

Yes, I can solve your problem, but you should check out the Shiksha college predictor first. https://www.shiksha.com/b-tech/resources/upsee-college-predictor.

Yes, your rank is good enough to get this stream here. You can apply for admission. Good luck.