NATA

Yes, you can, but only through management quota.

Yes, you are eligible to write but if you will not pass before the counselling then it is difficult to take admission there.

I would suggest you go for B.Sc or any other Bachelor's degree course instead of any engineering degree course.

Kindly be specific.

Yes, you can get a college, but not a good college and you can get private colleges by paying some extra fee.

Yes, the minimum score required for TCS, Madurai in NATA examination is 80. As you have cleared the cut-off range for this college, you can easily get admission.

Hi Abhinit,
As you know, Sir J J College of Architecture is one of the best architecture college in India, so seats of this college are occupied by the top rankers. Although your score in JEE mains paper 2 is good, but getting a seat with this score is difficult. For your satisfaction, you can participate in the counselling process upto last round or spot round.
If not getting any seat in this college, then go for good private colleges like amity University or lovely professional university for bachelor of architecture courses.
Best of luck.

Yes, the criteria for getting admission in Bricks College is 40% marks in NATA test. As you are having good marks in NATA you can easily get Bricks College.

Kindly visit this link:
https://shiksha.com/b-tech/resources/jee-mains-college-predictor