Engineering Entrance Exam

It is not possible with this rank. You should score maximum to get admission. They have various branches but every branch's cut-off is high and not below JEE Mains score of 240.
If you score 250+ then hope to get a branch but not CS.

All government colleges take admissions on the basis of the entrance exams result. Since you didn't give one it is highly unlikely now. One thing that you can do and don't place your hope on it. You can wait and later contact the colleges to see if they have any seats vacant or they are conducting spot counselling.

You have good marks in JEE. You can get government colleges of your state it's better to try once in the state-level counselling. Taking drop is not a good option because to get NIT, you must have 75 percentage in 12th so if you take a drop, then also you will not get any NIT software scoring good marks so if you take a drop, you should also try for improvement in board exam, then it will be beneficial.

IIT tag is surely worth a year but only if you are willing to sacrifice most of the things. Hard work always pays. But on the other hand, if you feel that NIT is worth it, then you should give it a try.

Don't worry, you are having 320 marks in JEE main, tou can try many private good colleges in south india, who takes only JEE main marks, like bannari amman college and many more!

You should study all the 3 subjects daily. Just divide your time accordingly because time management is one of the most important factor for JEE preparation.

https://www.shiksha.com/b-tech/resources/comedk-college-predictor
Please go through the link that I am sharing here to know about the same.
Good luck.

Keep on trying till the last round. All the best.

Yes, you can get any of private college you want to go with. Because in private college, you can take admission without any entrance exam. But JEE marks valid only for one year. So, you only can join private college.
Good luck.