Colleges in Pilani

Hello Prem,
Excluding BITS, colleges that accept BITSAT score are NIIT Neemrana and Tolani Maritime University.

BITS, Hyderabad is the best option for you.

As a BITSian, I can easily say that all three branches are equally good at Pilani campus. However, if you are evaluating on criteria of and opportunities, and placement records then following are my recommendations in order of precedence: CS, Electronics and Mechanical.

Yes, BITS is a reputed institute for engineering.

You may refer to the following link for details on admission process for international (Non-Indian) students:
http://sites.bits-hyderabad.ac.in/internationalstuadm/eligibility.php

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.

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 on your CGPA and the administration.
If you get the above CGPA, there is an option to change your course also.
All the best.

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