B.E.

Yes. It has an institution which is leading in region. Along with the factor of being popular, the added advantage is that is part of a university campus which itself adda to the vibrancy of study.

You should be scoring more than 130 if you are from general category.

It's good to read that you have clarity on your future goals. Since you are keen on moving into academics line, I would advice you to appear for the UGC NET exam and enroll as a research student in a university. This will not only get you stipend but also give you the desired teaching experience.

The fee of management quota is decide by the college management which is in the form of donation to take admission in best state government college of India. The fees is near about 70k but the semester fee is same for all, if you are from a poor family then you can take admission through tuition fee waiver. The general fee for all is about 30k per semester for all and 7k for tuition fee waiver student in government colleges.

No, there is no entrance exam for B.Sc physics. You can get a seat. Merit list would be prepared on the basis of your class 12th marks.

You can check on college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Link is here
Good luck.

There will be a separate admission portal on https://www.tneaonline.in/ for other state students applications. So, you can apply through that only. Keep a track of the website for updates.