"Å dra" can translate to both "to go" and "to leave" depending on the setting. When you're going from somewhere that also means that you're leaving that place.
In this particular sentence, the focus is not on the place being left, but on the place that the person is going to. Because of this the most natural way of translating it is "Are you going home?". Another accepted translation is "Are you leaving for home?", though that would be a less common way of phrasing it.
The way it was explained to me, is that hjemme is always an adverb. "Hjem" can be also an adverb and you use it when indicating a direction. "Jeg drar hjem" = "I am going home" vs "Jeg er hjemme" = "I am at home". But there is also the noun "et hjem" = "a home". It is confusing to me as well, hope that explanation helps
Yes, that is how I was taught too. If it implies movement it is hjem and if it implies location it is hjeme.
Jeg drar hjem - I go home (motion) Jeg er hjemme - I am home (location)
Other examples of "stedsadverb in motion/location form:
inn/inne ut/ute opp/oppe ned/nede bort/borte
There's something wrong... I had to say the sentence using the mic... probably my pronunciation wasn't enough good, but what does it mean... the translation is... I didn't have to translate, just talking. I was wrong, OK, so what? I don't know what my mistake was... it didn't help me to correct my mistake.