Translation:An bhfuil áit nua-aimseartha agat?
An bhfuil áit nua-aimseartha agaibh? An bhfuil áit nua-aimseartha agat? Do you have a modern place? Aren't they both correct?
They are, though the first is plural you and the second is singular. I think in English the singular is assumed, so 'agat' is the more natural translation
Why doesn't "Tá áit nua-aimseartha agat?" work? Is it just that that only works for the non-question version of the sentence?
You have to use the interrogative participle (an in the present tense) to turn it into a question, you can't just use tone of voice to indicate a question (though as all Irish speakers are bi-lingual, and will be used to that habit from English, you might get away with it in some circumstances, it would be a form of Béarlachas).
if they mean you plural (Agaibh) then the question should read "ye" not "you" as ye says you plural where you just
No, it shouldn't. The 2nd person plural in modern standard English is "you", not "ye". Even the minority of people who say still say "ye" typically write "you". Duolingo will usually accept "ye" for people who want to translate agaibh or sibh etc as "ye" rather than "you", but not all exercises have been updated to do this.
As it happens, the default translation for this sentence uses the 2nd person singular agat anyway.