Marked wrong for "Do you have a balcony in the apartment?" (with "the" highlighted as the error, and "Do you have a balcony in your apartment" given as a correct answer).
Possession is as clearly implied in the English as in the Russian; it'd be rare to find someone who has a balcony pertaining to someone else's apartment.
In case it's not already added, "at" should obviously be available as preposition too, though I erred on the side of the literal "in", myself.
Edit: Now tried that, and was marked wrong for "Do you have a balcony at your apartment?", with the preposition marked as incorrect.
Strictly speaking I can live in an apartment, which is not mine. Still having my own apartment elsewhere. So, the first apartment would be "the apartment" but not "my apartment". In Russia (not in Russian per se!) that may be quite a distinction.
But for the purposes of this test I think you're right.
Still marked "the apartment" wrong, two years later. I thought implied possession (no pronoun needed) only held for body parts and family members. Shouldn't this be свой балкон to be "your apartment"?
(Edit: I seem to remember the construction "у pronoun в place" and am trying to find the notes...)
In American English, when an apartment has a balcony, that means that the balcony forms part of the exterior of the apartment walls. You walk through a door from the interior of the apartment onto the balcony. That idea can be expressed as Duo suggests, "Does your apartment have a balcony?" or it can be expressed as "Is there a balcony on your apartment?"
If you ask, "Is there a balcony in your apartment?" that question asks whether there's a balcony inside the apartment - something which is possible in a two-level apartment.
If you ask, "Is there a balcony at your apartment?", this questions asks whether there is a balcony anywhere on the outside of the entire apartment complex - it's not limited to just a single (your own) apartment. As a result, it's not a question that normally would be asked.
The most likely question is thus "Is there a balcony on your apartment/Does your apartment have a balcony?" Either of those is natural and normal.