I think the first sentence is fine. For the next two, it depends on what exactly you are are trying to say. If you are trying to communicate a general fear, you could say either of these 1) I am afraid to be home alone. 2) I am afraid when I am alone in the house. But if you are trying to say specifically that you are currently home alone and that you are afraid you would say something like 1) I'm afraid because I'm home alone. 2) I'm alone in the house and afraid. The first is more specific about why you are afraid - because you are home alone. In the second case it may be that you are afraid for some other reason, but also are alone in the house.

First sentence is correct,2nd and 3rd should have been like 'i'm afraid because i'm alone at home' or 'i'm afraid and alone at home'