"Bist du immer noch nicht weg?"
I'm confused, if the translation is "Are you still not gone?" what's immer doing in the question? Shouldn't the question have been "Bist du noch nicht weg?"
Both your suggestion "Bist du noch nicht weg?" and the question in the exercise "Bist du immer noch nicht weg?" are fine. The English translation is identical for both sentences.
noch = still
immer noch/noch immer = still
The "immer" is just used to intensify the "noch". It can't be translated literally into English. Maybe in spoken English, you could emphasize the word "still" to achieve a similar effect: "Are you STILL not gone?"/"Are you not gone YET?"