At minimum, a parish is a geographical region which worships as a unit within the local Church (Diocese). As such, it seems the absolute minimum required to express the reality of "parish" is a priest, a mass kit, and a location for the faithful to gather and worship in celebrating the sacrifice of the mass.

Anything else which aids in this mission is a worthwhile addition, but is ultimately unnecessary.

Anything that does not add to this mission is not only superfluous, but may even be harmful.