"Whose is this tea" is quite a formal way of asking, and a more literal direct translation of "Czyja jest ta herbata?" but regular English Joe's will say "Whose {thing} is this?", both are perfectly fine. but the latter is the more common translation in English, and it just sounds better.
If I put "Julesa jest ta herbata" does it become "This is jules's tea"? Or would that just be "Ta jest Julesa herbata"? How would you ask if this is Jules's tea?
Yes. It has to match it in terms of gender, grammatical number and case ("Czyją herbatę pijesz?" = "Whose tea are you drinking?" takes Accusative, for example).
Well, the literal translation of "Czyja jest ta herbata" is "Whose is this tea", and you can always substitute 'this' with 'the' when translating Polish "ta"...