NIT

Maybe you can get in lower NITs or in Eastern part NITs. If you don't get in JoSAA rounds, surely you will get in CSAB rounds . So do the choice fillup smartly.

You can expect NIT-Warangal and Raipur. This rank is enough for admission to any of these NITs.

Here is the list top NITs for Civil Engineering Science
1National Institute of Technology, Tiruchirappalli
2National Institute of Technology, Warangal
3National Institute of Technology Karnataka, Surathkal
4National Institute of Technology Calicut
5Motilal Nehru National Institute of Technology Allahabad
6Visvesvaraya National Institute of Technology, Nagpur
7Malaviya National Institute of Technology Jaipur.

No, it can't be regarded as NITs. However it can be said to equivalent to some of the very new NITs, that to in near future. However NITs are the top and Apex of JEE Mains.

They will take a call on your admission according to the category rank in CSAB round.

NSIT is quite good for CSE. Top 5 NITs are better than VIT. VIT is better than other NITs.

Those are good nits but you can go for NIT Warangal.

Go for the branch in which you are interested. Think about the college after that. You have to learn that for 4 years. If you choose any non-interesting branch, then you can't do good. Go for interest, not for placements. Don't worry about new or old. You can apply for jobs outside also. So, choose the branch first.
Best of luck.

You have scored well in JEE and you have scored a great rank and yes, you can get a seat in NITs.