NIT

No, unfortunately it will be quite hard for you to get NIT with 37000 OBC rank, but if you are planning to go in other prestigious private universities then you can surely apply for it. Log on to Shiksha. In then you will get the information regarding how you can get the admissions in the private universities.

No, I don't think so. Check the cut off score in site.

You should have at least 75% in 12th standard. And ofcourse the entrance to NIT is mainly based on your JEE Main score. All the best.

No, with the rank of 46561 JEE Mains, you will not get admission in IITs and NITs even if you are in SC Quota. Because the cut-off for SC quota is High this year. Best of luck for your future and if there's any query, feel free to ask. Do upvote if you like the answer.

To check the list of probable colleges you can get, check the link below :
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

Please refer the below link to know the expected college you may get:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

You'll be able to get some good niits in the 2nd or 3rd round.

It's very nice to hear from you that you are interested in doing your graduation in engineering from any NIT. For this, you have to register with JoSAA. This entity has kept cutoffs for SC category for this at 54.01. Now, your dreams are possible if your percentile is this or better than this.
Best wishes to you.

Jahnavi, you can use college predictor tool to know the same:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

Follow the college predictor below for details:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.