Colleges in Rajasthan

50 mark is not enough in your category. You cannot get NIT or government colleges with this score. You can get private colleges.

With such a low rank, it will be very difficult to get CSE in a good government college. You can only get lower branches in good government colleges and chances of them are also very less.
Hard luck.

Dear V,
Please go through these links to predict the college you can get.
Rank predictor: https://www.resonance.ac.in/answer-key-solutions/JEE-Main/2017/jee-main-2017-rank-predictor.php
College predictor: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Dear Yatin,
Please go through these links to predict the college that you can get.
Rank predictor : https://www.resonance.ac.in/answer-key-solutions/JEE-Main/2017/jee-main-2017-rank-predictor.php
College predictor : https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, it is worth to study at BITS, Pilani because it is an international university and it is recognized world-wide. You can get better placements and a lot of knowledge with a great exposure.
NITs are better in terms of fee and education but not better than BITS. NIT is a government college.

You cannot get admission in a government engineering college. Try for private institutes.

No, BITS, Pilani doesn't offer mechatronics.

For the first year, I'm not sure about the fee concession. Maybe your BITSAT score can be considered. If you are a board topper, then you will a get full fee waiver.
But from the next semester onwards, if your CGPA is above 9 or 9.5, then you will get mess fee and hostel fee waiver. But this depends

You can get the fee structure on the official website. Yes, there is fee concession on the basis of class 12th score.