JEE Main

https://www.shiksha.com/b-tech/course/b-tech-in-mechanical-engineering-national-institute-of-technology-surathkal-mangalore-61468
Refer NIT Surathkal BTech Seat Matrix 2018 for rank range for home state quota and other state quota in various rounds.

Yes, you are eligible for both JEE Mains and Advance.

Surely you are eligible to give the exam. But you will be disqualified in the document verification round at the time when you report to the college. Hence you should not give JEE Mains.

The only criteria is that you have to fill the form for counseling as per the notification by JOSAA and pay the required fee. Yes, OBC candidates get benefit of their category. Hence there are two ranks - general rank and category rank.

Hi,
It's not a very good idea for you that you repeat one more year. It will be wastage of time. Generally, what happens is students whose ranks are within 2000-5000 they want to improve their ranks so they repeat the year. You must sit in JEE Mains counseling if you want a college. Enroll yourself for REAP counseling. You can get some good colleges in Rajasthan. You should even enroll for the state counseling. Don't go for VIT or SRM.

Since you won't get top NIT's through Mains rank, it's better to go for IITs. Since IIT is a brand, you will have more options in IITs and only in top NITs. Since you won't get top NITs, it's better to opt any IIT.

You can use this link to check out your chances of getting this college. This is shiksha's official college predictor tool based on previous year's data.
https://www.shiksha.com/architecture-planning/colleges/b-arch-colleges-india

1. Don't waste your time in books.
2. Complete the assignments given by the institute.
3. Clear your doubts, etc.

You can use this link to find out which colleges you can get from these marks. This is Shiksha's official college predictor tool based on previous year's data.
https://www.shiksha.com/architecture-planning/colleges/b-arch-colleges-india