Oh god, this traveling section has me so giggly. Bil in Dutch means butt, so this whole sentence looks like I have a butt to me. Then there is the word for bike, cykel, which sounds exactly like the Dutch word sukkel, which means idiot/moron/dumbass. So if I ever travel in Sweden, to me it will just sound like a lot of butts and morons.
It's the same with Dutch and German. Dutch 'huren' (to rent) looks like German 'Huren' (Whores). Dutch 'nuttig' (useful) means "slutty" in German. And then you can greet people with 'Hey, ❤❤❤ ... gaat het? (how are you) :D
Also a dutch friend told me a story of german students in the Netherlands talking to each other, saying "Ich hab' mich mit meiner Schwester verkracht, die soll mal klar kommen" (I had a fight with my sister, she should calm down) - but to the Dutch it sounded more like "Ik heb mijn zuster verkracht en ze is klaar gekomen" (i raped my sister and she had an orgasm).
Looks like we can use this "general sense" of car to be intentionally ambiguous about how many car(s) we might have, while still conveying that we are "car-having" :) If we don't want to be ambiguous, we can use the singular or plural sense instead. Is this true of the Spanish phrases you mentioned, or is this only a Swedish power?
It also works in Spanish. The question "do you have a car?" in Spanish it would typically be without the "a": Tienes auto? (o carro, o coche, depending on the country). It works in everyday sentences, like "I got here fast, because I have a car" - "Llegué rápido, porque tengo auto".
In spanish you use it to give the general sense of you having 'something'... Meaning there's no need to specify how many of those things you have. It might be the first or eighth you buy and you could still leave out the article. It's a matter of focusing on the action... May be... E.g. We can not go to the other city... Yes we can... And there you would say... I have something... (something that allows us to go)... I'm guessing you use it in that same sense in swedish... Let me know and if this perspective helps... =)