Psychology

You certainly can. If you are in your final year of PG, then you would not have to drop your current PG course. If you are in the 1st year, even then, it will be fine. Your interest in the subject matters more than the time. You can take admission in M.A. Psychology easily as it doesn't have any special criteria.

Did you pursue biology in your 12th? This sudden change of subject and stream will not be easy. You will have to pursue B.Sc. in psychology to be eligible of Masters.

Hello Venkatesh,
PG in psychology after BE? But why change subjects? I am afraid, psychology is a very specialised subject and some grounding up to the level of graduation is indeed required. Hence I would like to advise you that just have a look at the eligibility criteria for this course from the website of your intended university.
Best wishes.

Yes, you need to attend classes regularly as it is a full-time course.

Yes, you can definitely apply for women's studies in NET.

If you are indeed interested and want to pursue this course, it holds a lot of career prospects. NGOs, Schools, universities, companies, in the training and development sector, psychology stands with great scope. There are diverse fields too such as career counselling, student counselling, academic counselling, behavioural patterns, mental health and emotional wellness, teaching and welfare organisations.

Please refer to this link for all the details:
https://www.shiksha.com/mass-communication-media/film-tv/exams/ftii-jet/pattern.

You probably can. As eligibility criteria is decided by the university itself and it can be different for different colleges. So, check with the college for this.