M.Phil Psychology

Hello,
Yes, you can apply for the UGC NET exam, because for Assistant Professor there is no age limit. But, make sure you can fulfill other eligibility criteria also. You can get the complete details related to the NTA NET exam from - https://scoop.eduncle.com/ugc-net-exam must visit to get updated. As per the exam guidelines, you should have Master's degree to appear for the NTA NET 2019 exam with minimum 55% aggregate marks if they belong to General category or minimum 50% aggregate marks if they are from OBC/SC/ST/PwD/Transgender category. Candidates who are enrolled in the post-graduation can also apply for the UGC NET exam. Aspirants must also follow age criteria for NET JRF I. e. 30 years. Reserved categories get the 5 years age relaxation.

You can go for an MPhil (regular) after completing Masters from IGNOU. Every institution has its own criteria but since IGNOU being the recognized Open University, its degree is acceptable by almost all other regular institutions.
Recently, UGC has announced that candidates who score 55% in their Masters are eligible for MPhil from UGC recognized universities. So you need to focus on getting at-least 60% in Masters to be in the safe zone (Only if you are a general candidate).
I would like to give you an advice that please go for Central Universities for M.Phil as the faculty in such universities is mind blowing. JNU, DU, BHU, etc. are there in this list.