Translation:Are you going home or are you already at home?
I am confused about usage of "nach" and "zu" since the definition of "zu" was given as "to/towards" earlier. How does "zu" mean "at" here? And why is it Hause but not Haus?
These are idioms, and Hause means home, while Haus means house.
Zu Hause means at home; nach Hause means towards home, moving towards home.
I put "are you going back home or are you already at home" as my translation. Es ist richtig, nein?
There's no difference between "nach Hause" and the adverb "heim". But be careful, "Heim" as a noun tends to (but doesn't have to) refer to an old people's home, a children's home or even an asylum rather than someone's home.
"Ich gehe heim" = "Ich gehe nach Hause" - "I'm going home"
"Er ist in einem (or just "im" instead of "in einem") Heim aufgewachsen" - "He grew up in a children's home"
"Ich bin zuhause/zu Hause" - "I'm at home". This could also be "Ich bin daheim", but my understanding is that this is mainly used in the south (southern Germany, Austria and Switzerland).
"Das ist mein Zuhause" - ("Das ist mein Heim", if you must use it) = "this is my home" ("Heimat", if you're talking about a region, state, country, etc., and there are other options which I just can't think of right now).
Are you going home or are you home? that's what i said and its practically the same thing...
I said "are you going home or already at your house" mindlessly, but, should It be accepted?
I am wondering why there are no more pronouncitaton excercises incldued in Duolingo? Has there been a change? I mean the type of excercises where you had to repeat a setence or a phrase for pronounciation check. what happend all of a sudden? not enough web resources?