"Do you have a house anywhere in the South?"
Translation:У вас є будинок де-небудь на півдні?
Somehow replacing де-небудь with будь-де in this question is wrong... Even though both mean "anywhere" in the sense of "doesn't matter where"...
Де-небудь means anywhere, as in, somewhere, but I don't care where, so we can use it in a question.
Будь-де means more like "at a random location", so it sounds really off asking "Do you have a house at a random location".
хата should also be acceptable, as that means house. Будинок is a general word for building.