Q: the cook from a restaurant or a cook from the restaurant...? This sentence doesn't make it clear to me whether the cook or the restaurant is definite. Some thoughts?
Maybe. That'd be "Han är restaurangens kock" or "Han är kocken från restaurangen" depending on whether you mean that he works at the restaurant or that that's where you met him (or something like that). Objects 'owned' by another are treated as were they definite, but can't take definite form.