Why is there no "att" before the "hyra"?
Behöver is a verb that does not want att for a following verb.
Is there a rule, or is it random which words need it and which don't?
Well, modal verbs don't need it. But for a handful of common ones, it's irregular.
Weirdly, in English, you can say something like "He needs not rent a car", but you can't say "He needs rent a car". I wonder if you used to be able to say that.
Anyway, that's how i remember this.
Do we say "He needs to that hire a car" in English? Cause that's sort of what att does, as far as I know.
Would "han behöver hyra bil" be wrong? Since I would think that, because you're just talking about a car in general, not a specific car, that you can just say "bil" and not "en bil"
I think it works and sounds OK, so I added it now.
Can you also say "han måste hyra en bil"?
Yes, that works too. There's a difference in meaning between måste and behöver in Swedish that you don't really seem to have in English, where native speakers tell me they use verbs like 'must', 'have to', and 'need to' interchangeably.