IIT

Yes, of course every branch is worth studying in IIT And NIT because IIT and NIT give quality education and help you to enhance your life goals.

There are many good colleges in India for computer Science other than the IITs and NITs. Here are some of the top colleges for computer Science in India:
BITS Pilani
IIITs
VIT
DTU
BHU etc.

It was a great opportunity to get an internship at IIT and not everyone gets it easily so to increase your chances of getting an internship at an IIT, research, prepare a strong resume, contact professors, apply for internship programs, attend career fairs and networking events, and be persistent in your efforts.

The fee structure is different for different IITs and different NITs. If we see on average the fee for M.Tech in IIT is around 1 lacs to 1.32 lacs INR. It may vary for some courses also. In NITs, the fee structure for M.Tech is around 40,000 to 70,000 INR.

Yes, it's worth that you are pursuing Mechanical Engineering but only from some top reputed government colleges like NSUT, DTU, HBTU, IET Lucknow. Otherwise, it's not much worth from any other college especially private colleges.

Yes, its worthing because there are many top government colleges like DTU, HBTU, where you will get a good exposure and a great placement from electronics engineering. If you only focus on the placement, the average package of electronics engineering in HBTU is 7.5 LPA and the highest package is 44.5 LPA given by Amazon.

For the general and OBC category the fees costs 2-3L in IIT and 15000 for SC/ST category in IIT. Whereas in NIT it costs 1-2 L for OBC category it costs and 10000-15000 for SC/ST category in NIT.

You have to study and learn as like IIT and NIT student there is no difference in your hardwork but 1 factor is different for you that is the company coming for placement. Big companies are not going to your college so that you have to go to them from your own. It can happen by hardwork and discipline.