Seems possible in some contexts, added.

Because "mężczyzna" is a man, so he's masculine, and the form of "który" has to match.

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.

no problem