Application for registration of trust U/s 12AA

1. A charitable trust runs pre-primary school since 2016. The other objects of the trust are running ambulance, library for needy etc. The trust is incorporated as per the MOU and not trust deed.
2. The trust is duly registered under The Bombay Charitable Trust Act.
3. They had obtained 80G and registration certificate at the time of inception i.e. in 1996. But never renewed it later as there was absolutely no activity in the trust until 2016.
4. Even after 2016, no application was made either for 80G or 12A or applicable section.
5. The school has gross receipts less than 5 crore. It's always been a few lakh rupees since the activity started.
6. The trust always filed the income tax return claiming exemption U/s.10(23C)(iiiad).

The queries :-
Whether the trust now requires to obtain registration 12AA/12A by filing an application in form 10A and 10 AB?
Whether the unregistered trust is entitle to exemption U/s.10(23C)(iiiad) as the gross receipts are less than 5 crore?

Please guide in detail so that the trust can decide upon its course of action accordingly.