I feel like the Hindi sentence could most naturally be translated as "my house does not contain a wall". In any event, the listed translation "my house does not have a wall" makes little sense in English. If someone said that to me I'd assume they meant it has no wall around the garden or something like that, not that it lacks an internal wall.
I disagree. A house refers to a building that may or may not be your home (meaning the place you feel at ease). When talking in first person you can make that distinction as well. EDIT: I talked about English. I know Hindi doesn't make this distinction. Regarding the translation: "house" sounds far more natural in the context of this sentence than "home" does.