"The staff of the restaurant"
You never have the definite article after a possessive word. That would be like saying ”the restaurant’s the staff” rather than ”the restaurant’s staff”.
You could say restaurangpersonalen (The restaurant staff) in this case. (Just one word) It does not have exactly the same meaning but they are fully interchangeable.
Yes. "Personalen på restaurangen" would work, but that would translate to "The staff at the restaurant".
It gave me "personalen på restaurangen" as the correct answer. So is that not correct? It should only be "restaurangens personal"?
No, it is correct. Just that if you translate it back you would most likely use at instead of of.
This one threw me off. I initally wanted to say restaurangens personal but tried personalen av restaurangen because usually the questions are picky about word order, i.e. to teach us how to say things in different orders.
We rarely use av-constructions like that. Like, when they say a cup of coffee in English, we just say en kopp kaffe. I wrote this somewhere else the other day: When av is used, it is more for materials, like ett hus av sten, 'a house made of stone' (stenhus is a more frequent way of saying it) or something that is meant to resemble something, like en bild av en blomma 'a picture of a flower'.
I think I answered that in my comment above (in answer to funtaco) – we just don't use av that way.