JEE Main

No (as per the last year's statistics). But many seats were left empty last year, so you may try to get a seat if you're lucky enough.

No, counselling is not done through JEE Mains. But you can get admission there on the basis of your JEE Mains marks or else you have to give the entrance exam.

Hello,
Well, you can use college predictors. One of the predictor's link is given below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
And also check the official website for opening and closing rank in the last round (round 7) for 2017 to know about your preferred colleges.
Here's the link:
https://josaa.nic.in/Result/result/OpeningClosingRank.aspx
And in 2016 over here:
https://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx

Follow the following links:
https://www.shiksha.com/b-tech/course/b-tech-in-civil-engineering-national-institute-of-technology-surathkal-Bangalore-61474
https://www.shiksha.com/b-tech/course/b-tech-in-mechanical-engineering-national-institute-of-technology-surathkal-Bangalore-61468
https://www.shiksha.com/b-tech/course/b-tech-in-electronics-and-communication-engineering-national-institute-of-technology-surathkal-Bangalore-61501
https://www.shiksha.com/b-tech/course/b-tech-in-chemical-engineering-national-institute-of-technology-surathkal-Bangalore-61489

Refer the link:
https://www.shiksha.com/college/national-institute-of-technology-surathkal-mangalore-24187/admission?stream=2&course=176330&sort_by=relevance&type=question

Good engineering colleges for you according to your scores are Modern College of Engineering, D Y Patil College of Engineering Akurdi, JSPM College of Engineering Hadapsar, Marathwada Mitra Mandals College of Engineering, etc.

If you are a Tamil Nadu resident than you will be eligible for Anna University or you can go for other private colleges. For government colleges you should have cleared JEE Mains and Advanced.

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.

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.