First: differentiate (spelling)
Take as an example, a university.
It is an institution. It exists only in people's minds.
The premises are the land and buildings that form the university.
Oxford dictionary defines a facility as "A place, amenity, or piece of equipment provided for a particular purpose". So a university may have a sports facility, including a gymnasium, which is also a facility. Lecture theatres may be considered as teaching facilities.
An amenity is defined as "A desirable or useful feature or facility of a building or place". So a swimming pool may be considered as an amenity, because it is useful. Amenity is more specific than facility. The sports centre (a facility) may include a gymnasium (an amenity).
In your example, the pavilion could be regarded as a facility, which contains a gym and changing room, which are also facilities, but also amenities.
"I think it would be considered as a priority to renew all (????) of our pavilion including the gym and changing room."
"as" unnecessary, but not incorrect.
comma useful after pavilion