My Czech friend said that this can't be a sentence on its own, because it has to have a pronoun. Can someone explain why this doesn't need a "to" or other pronoun?
Your Czech friend is wrong. There are to posibilities:
The pronoun is understood from the previous sentence.
It could mean "There are no women." or "We have no woman.", but that is unlikely for women. However "Není chleba." "There is no bread." is perfectly natural.
Why not "those are not women"?
That would require some pronoun like: "To nejsou ženy."
So here I can use the pronoun ony, right?
"Ony nejsou ženy" is accepted.