The first is correct only if he is literally moving a house from on location to another, on a very large truck, or something like that. You probably want, "Which/what house did he move to." The second is correct, but you probably want a different tense: Why is he moving? "Why does he move" sounds like moving is a continuous activity that he has done in the past and will continue to do.

对的方式如此： Which house did he move to? Why did he move?