NIT

According to new eligibility condition either candidate have 75% + marks in class 12th or you have to be place in top 20 percentile in your 12th class board.

You can use this JEE Mains college predictor tool
to know the available shortlisted colleges based on your marks.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

I don't know about IIIT, so I won't talk about them. As your home state is Haryana, you can easily get NIT-Kurukshetra's ECE and EEE branches. Of both the branches, I think ECE is better. But it purely depends on your interest.

Hello Sai Krishna,
As per your rank, you will surely get good branches at lower NITs, however, check here to know more.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Hello Tripti,
As per your rank in JEE Mains and Advanced, your chances are slim to get any NITs or IIT's, however, check here for more insights.
JEE Mains
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.
JEE Advanced.
https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

No, you can't do it after completing B.Sc. You can get admission in MCA in NITs. For Masters, you must have a graduation degree.

Hello,
Greetings from Shiksha for getting into NIT. You should have a minimum percentage of about 65% in tour +2 standard i.e. your intermediate second year with maths as a subject background.
Goo luck.

Definitely, NIT Nagpur. If you are looking for good faculty members and placements.

Yes definitely, if you want, you can pursue MCA from NIT since, you have done B.Sc in maths. But the condition is that you have to qualify NIMCET examination to pursue MCA from any of the 11 NITs providing the same. The NIMCET is a National Level Entrance Test conducted by NITs for admission to the MCA course offered by NITs. Only if you are capable of qualifying the exam with a good rank, you will be able to get an admission in the NITs.

Hello Dear,
Here is an article by Shiksha authors about top engineering colleges along with their rankings, fee structure and placements. Apply the filter to get desired results.
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0