JEE Main

With this ranking, you will not be able to get an NIT as the marks seem lying around the cutoff. You should apply for state government colleges or autonomous institutes. Moreover, trying a seat in lower NITs such as Manipur and Silchar will not be worth it for distance education.

With a free seat, we can assume a seat with tuition fee waiver by the government. In private colleges, the scheme is dependent on their own norms and that varies accordingly. For government colleges, full TFW is given to ST and SC students. Moreover, there are some government schemes which also give scholarships to their state student with such good rankings. Kindly get through it. Thank you.

If you are from general category, then no, as all the government and semi-government colleges filter on the basis of JEE Mains marks.
Also, with these marks, don't take a government college if you are getting it, as it will not be worthy.
Choose a big private university for its placement or take a year drop.

No, just JEE rank can't be the base for admission in this university.

You can't go for admissions with a reappear. You need to present a passing result first.

https://www.shiksha.com/b-tech/resources/wbjee-college-predictor
Check the college you can get with your rank.
It would be better if you take admission through WBJEE rank as you will not get any college through JoSAA.
All the best.

No, in Tamil Nadu, the best college is NIT Trichy and Anna University. For both it is difficult as for NIT, the minimum marks are 75% in HSC and around 4000 all India rank for B.Arch. I would suggest a private college in Bangalore or Hyderabad.

There are very few seats for general in both the colleges. Also, in NIT, minimum board percentage should be 75%, so you will not get NIT.
For Sir JJ, the admissions are through 50% board + 50% your competitive scores. Your board percentage seems less, so the chances are very thin.

There is every year cutoff, depending upon students and total no. of college seats available. Though, you can expect a cutoff around 85 i.e. minimum marks to get through JEE Mains.

Mere clearing the JEE Mains will not lend up any college across the nation, atleast a good one. Kindly mention your precise marks to get the best suggestion. Moreover, you can use the college predictor too for searching the colleges.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor