"Can I rent the car?"
Translation:Kann ich das Auto mieten?
Technically that's "May I rent the car?". Kann is asking if it's physically possible, Darf is asking if you're permitted to. There's some pedantry about the distinction between these in both languages, but you can avoid all that by just keeping the translation as direct as possible.
Because they do not mean the same thing.
A Fahrzeug (vehicle) is a broader category and includes not only cars but also busses, trucks, bicycles, etc.
It would be like translating Hund as "animal". Sure, all dogs are animals, but that doesn't make "animal" a particularly good translation of Hund.