Electronics and Communication Engineering

No one can guarantee 100 percent placement. Although, colleges project so.

EEE degree syllabus concentrates more on Electical engineering. Graduate have job opportunis in Electrical and Electronics industries only. BTech ECE provide more job opportunitie in comparison to EEE because in addition to electrical/ electronic industries graduates can also be employed in Telecom and IT industries.

Yes you can join aviation industry. You may do multi dicipilanary MTECH in Aerospace degree offered by various universities. You can join Indian Air Force in Aeronautical Engineering (Electronics) branch also. IAF will train you on avionics and related fields.

Yes, you definitely can apply for engineering colleges in Mysore. Here's the list of college which you can get with your COMEDK score
1) Vidya Vikas Institute of Engineering and Technology
2) Maharaja Institute of Technology Mysore
3) NIE Institute of Technology

Hi
ECE engineers are in demand because of several reasons. The list of core companies can be found on this link. Explore it well to decide.
http://www.regencyengg.com/ecejobs.html