It depends on the role in sentence that is realized with different cases - variations of the same word. Different the role in sentence or preposition before noun, different is the used case. Sometimes You can treat cases as noun combined with preposition in one word e.g usually in construction done x „with y” this „done y” is translated with Instrumental.
There is no such thing like mężczyźna. Mężczyzna is nominative singular. Nominative plural is „mężczyźni” - probably this is what you meant.
i cannot reproduce this error after completing it once, but i wrote twice in polish, getting the following error: "you wrote in english, not polish",
then i tried in english and got the same error,
then tried again in polish and it was finally accepted.
i'm not sure how this is possible, but i think i wrote "ktora" in the first two attempts, then "ktore" in the last attempt (i know both were wrong)