"Who is going to the market?"
Translation:Quis ad forum it?
Ad shouldn't be dropped, however, domus is one of the nouns that is able to use the locative (domi). Nouns that use the locative are able to drop the ad for the place to where construction and a/ab for place from where construction.
Quis in foro est? but Quis domi est?
Quis ad forum it? but Quis domum it?
Quis a foro venit? but Quis domo venit?