Telecommunication

Yes electronics and communication and electronics and telecommunication are same. They can apply for ECE stream related jobs. There is no difference in that.

Yes, it's correct that getting a job in core electronics is difficult (but not impossible). IT jobs are easily available in comparison. To get core job you can appear for GATE and score good and get into PSU sector. This is one option you can look.

You can choose your course according to your interest.
If you are interested in engineering, then go and start your career in your interested branch.
If you are interested in teaching and research program, then go for B. Sc with any principle subject.

BITS Pilanu offers B.Tech Engineering Technology, a 7 semester Work integrated Learning Programme delivered online designed to provide a broad intellectual foundation and contemporary technologies while developing relevant engineering fundamentals, and introducing the important methods of technology practice. You may look for details of program at: http://www.bits-pilani.ac.in/uploads/WILP_Brochures/2016/B.Tech. Engineering Technology.pdf

You can join BSNL, Airtel and any telecom company.

I think it is possible in countries like Germany, Ireland and Canada. Some colleges in these countries won't ask for GMAT or GRE marks and they'll admit candidates with IELTS, Past academic performance and work experience (Mandatory).

You can wait for final rounds, where internal transfers happen and you can surely get IT as vacancy always opens up in the last round of admission.