What would "żadna kobieta tu pracuje" mean? Would it be correct Polish or is the double negative essential?
Yes! The double negative is essential. It is as if there are two verbs: " pracować " and "nie pracować ". As if the adverb "nie" was part of the verb." Sometimes occurs even triple negation. For example: nikt nigdy tu nie pracował = No one has ever worked here.
Hmmm... a similar "no women" version was accepted, so "no woman" should be as well, I guess.
In Russian, żadnaja means greedy, so it sounds like a greedy woman doesn't work here. :-D
Read above. If "not a single woman" works, then I'm sure "not one woman" is also acceptable