Robotics

Yes, you can join and M.Tech robotics has a great scope at this point of time.

You can check out the links below for details as you have not mentioned which institute you are aiming at MIT-Pune or MIT-USA:
https://www.shiksha.com/college/Maharashtra-institute-of-technology-kothrud-Pune-23583
https://studyabroad.shiksha.com/usa/universities/massachusetts-institute-of-technology

Yes, you can. Many mechanical engineers are pursuing their careers in the field of robotics.

Check the list of all Robotics Engineering colleges/institutes in Karnataka listed on Shiksha at the link provided below. Get all information related to admissions, fees, courses, placements, reviews & more on Robotics Engineering colleges in Karnataka to help you decide which college you should be targeting for Robotics Engineering admissions in Karnataka. https://www.shiksha.com/engineering/colleges/robotics-engineering-colleges-karnataka.

S, PSG is affiliated to Anna University, Chennai. And, Anna University has an other state quota for all its 500+ affiliated colleges. The guidelines are as outlined here:
https://www.tnea2018.in/tnea-2018-for-other-states-b-e-b-tech-admissions-in-tamilnadu/
So, yes, depending on your cutoff, you can get a seat in PSG College of Engineering through TNEA counselling. Hope this helps you and all the best!

JEE Mains 2018 College Predictor
Use your JEE Mains 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of JEE Mains 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

There are only two colleges for robotics, PSG College of Technology and Coimbatore Institute of Technology. The top college for robotics is Coimbatore Institute of Technology.