Translation:I am not going home. I am already at home.
I am not sure, but it may be because you have to say that at the current moment you are not going home. At this can be expressed in English only by using the Present Continuous.
With this longer phrase, I'm not sure what I got wrong. I feel it might be that I wrote, "I'm already home" which should be valid.
why not zum Hause. Since Hause is masculine, and zu takes the dative, then we should have zu+dem Hause, no?