The English translation should read "Have you paid this month's /house/ rent?"
Yep, that's exactly what I put. We don't usually use these long constructions in the form "the X of the X"
I put, "Have you paid the rent this month?" they didnt like that formulation either :-P
Yes, it's unnatural to specifiy that it's on the house, because what else would rent be on? And it should be on the house or apartment, rather than "of".