From the dictionary definition: A home is "the place where one lives permanently, especially as a member of a family or household." A house is just a building. Also, one says "I am going home", it would sound awkward to use house ("I am going to my house." ?!)
Not exactly, since your sentence is comparing “your house,” whereas Duo is comparing “yours.” This exercise is to practice the use of “seninki” so that’s why your answer probably isn’t accepted. In the sense of “do they tell you the same fact” then yes.