NIT

As far as I know, no colleges in India concentrate their entire Masters course in pure mathematics. But they do provide abstract papers as a part of the syllabus. Further if you like any paper, you can go ahead and start reading more about that paper. Almost all the NIT's have very similar course structure. National Institute of Technology Calicut will be your best BET. Regards.

For admission in NITs, one should have good marks in JEE as the NIT are the 2nd top colleges of india of engineering and technology. Please check out this link to predict the colleges based on your rank in JEE. But you should have to apply in NIT for admission.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=6919840

Your rank must be 55000 and not score, with this rank, it's quite difficult to get into an NIT, still, you can check through the college predictor link below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can by clicking this link mentioned below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

You need to check the college predictor below to verify:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
*Getting NIT with this rank is quite difficult.

Congratulations for your percentage in class 12th. But I'm sorry to say that your JEE Mains score is too low to get admission in NIT
Try in some good private colleges which take admission on the basis of class 12th PCM marks.
Good luck.
Upvote if it is useful.

Yes, might be. You can check this college prediction link so that you have a rough knowledge of getting a college with this rank:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Your chances are less of getting NITs but you can get colleges of your state, may be government colleges. Try JEE college predictor to get more information and insight about college & branch which you can get on the basis of your rank:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=4067795

Kindly visit this link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor