Hi.

Ofcourse you can pursue PhD in Electrical Engineering as long as you pass the entrance examination as well as the interview to get an admission in desired institute.

Incase you have further query regarding the PhD admission procedure of a particular institute, please feel free to comment.

Most probably not!  But you can do interdisciplinary fields and open question of electrical engineering. This is entirely dependent on your advisor.

You can do MTech courses after MSc in some fields dependent on the university eligibility criterion.

I hope my answer helps you. All the very best for your future endeavors!