"pytać" is to ask a question. "prosić" is to ask for something, to make a request.
I've heard that Poles are more and more omitting "o" in speech. So, instead of "czy mogę prosić o menu?" you'd hear "czy mogę prosić menu?" Is this acceptable?
With this specific verb, "prosić" (and "poprosić") it seems acceptable (probably more colloquial). But better don't stretch this to other verbs, at least without asking first if it's ok ;)
Actually it sounds to me like "Can I ask for menu" vs "Can I have the menu".
Is it possible to use here: "Twój mąż prosi odpowiedź" and "Twój mąż prosi o odpowiedzi"?
"prosić kogoś" means to ask someone, "prosić o coś" means to ask for something.
Hence, "Twój mąż prosi odpowiedź" translates to "Your husband is asking the answer" (whatever this means, presumably there is a personified answer in the room).
"Twój mąż prosi o odpowiedzi" means "Your husband is asking for answers".
In the first case, I'd still say 'Twój mąż prosi o odpowiedź A' (meaning 'answer A, please' as opposed to 'dear answer A, could you please...')
Czy są poprawne, since you ask about two things :)
"prosić na odpowiedź" - nope.
"czekać na odpowiedź" - yes.
Note that it's a Ź (with an accent), not Ż (with a dot). That's not visible well with this font...
"Requesting" was marked wrong, but I think that's the same as "asking for."
I wrote "your husband is asking about the answer", and based on this thread, it makes sense that for is better than about. But there's another exercise in this lesson with "o co" and "about what" was accepted. Is for really the better choice there with this verb?