There is as such no free education.

There is exemption of tution fees in IITs for reserved category and private colleges provide scholarship program to top rankers.

Choosing  a branch totally depends on your interest. Every branch has good scope in the future for a right candidate.

Mechanical branch is one of the oldest and evergreen branch in engineering. It has very good scope in the future. There are plenty of jobs available in the market in mechanical engineering. Both private and public sector have good opprounitity related to jobs.

Freshers can get a package of around Rs. 10,000 to 25,000 per month with experience you can get around Rs. 40-45 lacs per annum.

Good Luck!!