what is eligibility for doing PHD? is there a part time option?

Answer 1

Actually the pursuit of a Ph.D. is a lifestyle choice. It requires intensity rarely seen elsewhere. Especially the creative portion wherein you create something Original, i.e. no one else (on the planet) has done it before. Lots and lots of time.

Eligibility, acceptance to a grad school. Basically a BA/BS with a GPA better than 3.0, and appropriate scores on the appropriate Advanced GREs. Although original research and the corresponding publication of that research smooths over many rough bumps.