"Do you have your own apartment?"
Translation:Hast du deine eigene Wohnung?
Yes, if you look at the previous comments, you'll see that both mindlapse and mauvebean tried to include a possessive adjective to correspond to the English “your”, and Hohenems gave correct versions for both informal singular and formal possessive adjectives for word-for-word translations of the English sentence.
But the curious thing about this exercise isn't that the idiomatic German sentence at the top of the page lacks a possessive adjective; it's that the English version not only contains one, but has to contain one: Even though possession is already made explicit by the verb ‘hast’=“have”, the defective English adjective “own” can't stand on its own, without the possessive adjective “your”.
"einzig" means "sole/only".
"Mein einziges Haus": "My only house".
"Ich bin der einzige Mann in der Gruppe": "I'm the only man in the group".
"Ich habe ein einziges Mal geraucht". "I smoked once".
The expression "Selbst deine einzige Mutter" is thus somewhat strange, as you emphasize something which is true for everybody. However, people say that sometimes for emphasis. In my opinion, it should be translated with "Even your only mother".
I would translate "Even your own mother" with "Sogar deine eigene Mutter".
Note that in other contexts "only" translates to "nur".
If you mean ‘Selbst deine eigene Mutter’ and ‘Hast du deine eigene Wohnung?’, then it does.
‘Hast du eine eigene Wohnung?’ literally translates as the ungrammatical English “Do you have an own apartment?”, meaning “Do you have an unshared apartment?”, which is unidiomatic. The closest idiomatic translation is “Do you have an apartment of your own?”
German doesn't need a possessive pronoun in this sentence, English does. So "Ich habe eine eigene Wohnung" is said in German, "I have MY own apartment/flat" in English. They mean the same because they're how everyone expresses this situation naturally. When German speakers say it in English, they routinely talk about "an own apartment", which sounds weird.