Masters

Generally the admissions happen between may to september, but since you haven't mentioned any specific college it might be inaccurate for every college. The admission dates vary significantly for different colleges depending upon exams and all these things.

In India there are many universities which offers Masters in nursing or pyscology online majority of these are mentioned below: 

IGNOU ( indra Gandhi National open University) 

Amity University 

Lovely professional University 

Chandigarh University 

Suresh Gyan vihar

Annaamalai University 

University in Mumbai 

Imts institute 

Parul university 

Nalanda 

University of Delhi and many more

GTTC mostly sticks to diploma-level stuff like Mechatronics, Tool & Die, and Precision Manufacturing. They don't really offer postgrad (PG) courses. But if you've done a diploma, you can either level up with advanced diplomas or go for lateral entry into engineering degree programs elsewhere. Basically, use GTTC as your base, then upgrade outside for higher studies.

Yes you can also apply the NET (National Eligibility Test) whatever the difficulty you are giving your 1 st year PG in June. They can apply under the UGC NET eligibility criteria even when they are in their final year of a Master degree or when they are awaiting results. But to get officially eligible to JRF/Assistant Professor on the basis of having passed the NET, you have to successfully take your Master degree with required percentage (55% in general and depending on the reservation which are 50%) within two years starting of the day the NET result is declared. Failure to abide, will translate to disqualification.