IIT

For your rank it is not possible to get in NITS but you have a chance to get into IIIT's 

Unfortunately, with a JEE Main AIR of 60,000, you cannot get into an IIT, as IIT admissions are through JEE Advanced, not JEE Main.However, with AIR 60,000 in JEE Main, you can target top NITs, IIITs, and GFTIs for ECE. Some good options include:-

1)IIIT Lucknow / IIIT Nagpur

2)NIT Raipur / NIT Goa / NIT Sikkim

3)IIIT Bhubaneswar (State quota)

4)GFTIs like Assam University

With an All India OBC rank of 84 and a Science stream (Math) background, your chances of getting into a top IIT are excellent.You can expect Top IITs like Bombay, Delhi, Madras, Kanpur, Kharagpur.Be sure to participate in JoSAA counseling and keep backups from IIT Hyderabad, Gandhinagar, BHU, ISM Dhanbad, etc.

Yes, Mechatronics is good in VIT Vellore as it involves a modern curriculum, strong labs and research, good faculty, and industry exposure. Mechatromics is equally good, I'm IIT, NIT with slight differences.

No. It is a myth that the difficulty level of the JEE Advanced exam will depend on the IIT that conducts it. The fact is - JEE Advanced paper is not set by a single IIT, but rather by experts from multiple institutes. Hence, one IIT is not responsible for the exam difficulty level.