Both are used. The second is grammatical.
My friend tells me he's moving his stuff. I ask him:
Are you done with school? Moving back home?
Are you done with school and moving back home?
Are both okay? Which one is more native?
Is the first grammatical?
Are you moving back home? - better?
Would a native speaker say or text : Are you done with school? Moving back home?
I would text: 'Finished school? Coming home?' but that is to save time and characters.
People rarely text grammatical sentences.