Cheap motels (in the US sense) that are near highways and are not "love hotels" will just call themselves "hotels" and avoid the sex-related stuff. There are plenty of those.
I think it's also pretty common place for people who meet at night clubs and don't want to take their partners back home (in order to keep their privacy). They go to the motel and that's it.
Wikipedia doesn't have a lot on this: https://en.wikipedia.org/wiki/Motel#South_America
Regarding Brazilian motels, I'm not sure about the etymology, but it is possible that it was borrowed from English, I guess.
Because people DO park cars there. In many (most?) cases, there are individual parking garages (with a door that closes) which open to the specific room. There are no elevators, corridors, or anything that would allow unrelated people to interact. Other than the 'reception', which is essentially a drive-through, you do not have to see or interact with any human beings. Even payment is handled through a small compartment.