"Men and women"
Translation:Mężczyźni i kobiety
"I" links parallel or equivalent items, e.g. "I skip and jump."
"A" introduces contrasting, elaborating, explanatory or supplementary ideas, e.g. "I'm a lumberjack, and I'm okay."
No, '"z" means 'with'. "Mężczyźni z kobietami" would be a way to say "Men (together) with women".
Also: from (z Polski = from Poland), out of (jeden z nich = one (out) of them), made of (dom z drewna = a house made of wood).
Those are in the genitive case. They're used for possession ("men's and women's"), counting ("ten [of] men and women"), and with various specific verbs and other situations.
To indicate "men and women" absent of context, the nominative case is expected. That's "mężczyźni i kobiety."