Electronics

Yes, it is available in online format too.

Yes, it is possible for lateral entry but it depends on college to college and university to university.

You can learn it from various institution, they offer a good programme, in BIG Data.

It is possible. Just choose GATE for biomedical stream, but for this you have study a lot since the exam will be based on the syllabus of bio medical stream only. And, you did your under graduation from electronic only. I suggest you to go for that stream, which will relate to your B.Tech branch. Otherwise, you may face some problems. Just stay in your branch and get specialization and knowledge by doing the Masters from electronic only.

Yes, you may get. You have a fair chances of getting a seat in IIT just wait for counseling procedure that is CCMT but I have doubt that whether this IIT offer this course in which you want to take the admission since many other IIT too offered this course but this IIT does't because last year also this IIT did not release the cutoff for power electronic. So I suggest you take just verify whether the course is available in the IIT or not. Also check other IIT like Delhi, Bombay this might offer seat in power electronic.

There are wide variety of options where you can switch to. First being control systems, then robotics, machine learning etc. You have to first decide your interest field.

There isn't anything as such. IISER is known in its own way. It can't be compared with other colleges and vice versa.