JEE

With your JEE Mains percentile and OBC rank, you can consider colleges like some NITs (National Institutes of Technology), a few IIITs (Indian Institutes of Information Technology), and several state-level engineering colleges depending on your preferred branch and location; some options include NIT Patna, NIT Manipur, IIIT Kottayam, IIIT Tiruchirappalli, and the Government Engineering College, Gandhinagar.

With a CRL rank of 159865 and an OBC rank of 53541, you are unlikely to get admission into a top NIT for a popular branch, but you might be able to secure a seat in a newer NIT for a less preferred branch using your OBC category rank; it's best to check the closing ranks of different NITs and branches on the JoSAA website to see your chances

No, there is no such provision to get direct admission in BTech courses at Netaji Subhas University of Technology (NSUT) (formerly known as NSIT).

 There is no provision for direct admission or management quota. NSUT is an autonomous government institute that offers 85% of the seats to in-state students and 15% to outsiders.

No. Generally for getting a good branch in NITs that are out of home state 200+ is must. Since, you have two advantages, home state as well as OBC NCL be sure to at least score 150+ in JEE mains. You will get your desired branch in VNIT. 

Mostly you should be allowed in until it isn't mentioned in the instructions sheet. But what I would recommend for safety is that carry an extra document in case they don't accept it like your passport with a recent photo or your college id along with the Aadhar card. But don't forget the Aadhar card, it is extremely important.