What is the purpose of "czy" here? Would "jesteś kobietą?" not be enough?
From my limited experience, "czy" indicates a yes/no question.
I think "czy" could be dropped, if you intone the final syllable of the final word in question form (i.e. rising tone).
That's exactly the case. Czy indeed indicates a yes/no question. It can also initiate a subordinate clause: I ask myself whether you are a woman = Pytam się czy jesteś kobietą. Note that when it initiates a subordinate clause czy is necessary.
Yes, it is. Also note that the use of czy to start a yes/no question is somewhat formal and most Poles don't use in everyday speech, but it's nothing unusual to use it.
I wrote "You are a woman" (which can be a valid question in English), and Duo marked it wrong. Does that mean that if the Polish sentence begins with "Czy", then the English translation must begin with the verb? (It must be "Are you a woman"?)
Yes. In the Polish sentence the speaker clearly has no clue whether he's speaking to a man or a woman, and your version sounds as if you just realized that you're talking to a woman and you're very surprised.
Cool. That's exactly what I was wondering, but I think you expressed it better than I did. :) Thanks!
A bit, only that as far as I understand it is not used very often in Russian anymore (at least it wasn't used often in the course), and in Polish it's very common.
The fast audio sounds like "Ty jesteś kobietą" and the slow audio sounds like "Czy jesteś kobietą".