Here is the table of declension: https://pl.wiktionary.org/wiki/m%C4%99%C5%BCczyzna You write "ź" in singular dative and locative, plural nominative and vocative.
"Człowiek" is "a man" as in "a human (being)". "Mężczyzna" is "a man" as in "a male person ♂".
Here you have plural "men", not singular "man". Plural of "mężczyzna" is "mężczyźni" (not the Z getting softened to Ź), and plural of "człowiek" is completely irregular and it's "ludzie". Which works here as well.
i am in poland and was finsing it very hard to learn... but i met two polish people that gave me one lesson on the sounds and one on the different plurals and what they are... and oh boy I am finding it much easier, i dont know why either, im finding polish is similar to italian sounds lol
Listen to them here: http://popolskupopolsce.edu.pl/lekcja/1/MAZOWIECKIE
z is like the English one, ż can be rendered by zh, ź (with an accent) will probably be the most difficult for you.