NIT

Nirma is a better option & after that JIIT Noida should be your preference.

Depends, in various NITs it is different. It is around 600-1000 for a single year.

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.

Maybe. Are you from SC/ST or another category?

There are many CFTIs in which you can get admission easily with this rank.

Yes, you can get an NIT if 7434 is your All India Rank.

Your results will make you eligible but sit for CAT, MAT or CMAT and crack the GD-PI.

For admission in NITs, one should get at least 75% in 12th and then appear in the JEE Mains exam and score a good rank in it. Previous years cutoffs for various NITs are on:
josaa.nic.in
Also for choosing NITs, you should visit josaa.nic.in on respective date of counselling as mentioned in the website of JoSAA. There you should fill up your choices
that is you have to arrange the various branches in various NITs as per you want them.
Best of luck.

JEE Mains 2018 College Predictor
Use your JEE Mains 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of JEE Mains 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

You cannot get any NIT or IIIT but you have another options for good private engineering colleges where you can get admission easily. Otherwise, you should go through the state counselling procedure for the government college or the best private college. All the best.
Thank you.