Also, because english has two forms, when you say "Listen" would mean something like "Man" is an object, a song, something.
When you say hear it's like how you feel knowing there is somebody getting home, closing the door, clapping. When you listen is to a song, to a recording.
One. The Accusative form is "mężczyZnę", normal Z.
There are some cases where it changes into Ź (palatalized Z, Z with an accent), but never Ż (zh, Z with a dot). Damn, the font makes them look so similar =='
Check the cases here: https://en.wiktionary.org/wiki/m%C4%99%C5%BCczyzna