NIT

There is only verification of medical certificate in NITs at the time of counselling but they may check through any medical board or can tell you to have a medical certificate from a valid government hospital. If your medical certificate happens to be fraud in any case then your admission will get cancelled and you may never be allowed to participate in JEE again and also, they can cancel the doctor license, if possible, in case of wrong information.

It is b hard to get a seat in NITs but you can try, as EWS is a new category this time and no one knows what will be its cutoff. Therefore, you can try in JoSAA or CSAB rounds.

Your marks are not that great and I don't think you have a great chance of making into the program being offered at NIT.

Getting an NIT will be difficult for you to with this score. I would suggest you predict the possible colleges here:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Best of luck.

Since EWS category is newly introduced, but you have chances in good branch and good colleges. So, you can go for counselling in GFTI, CFTI or reputed state government college.

No, you can't get NIT with this percentile in JEE Mains.

Yes, sure your admission is confirmed in NIT because you belong to the SC category.

It is hard to get CSE with this rank in any government college but you may try for NITs, Silchar, Mizoram, Meghalaya, and Nagaland.