"They say that they hear voices."
Translation:Oni mówią, że słyszą głosy.
Yes - generally in Polish subclauses are separated by comma, with a few exceptions.
Correct if what you wanted to say is "They will say". Perfective verbs cannot be used in the present, the form that you could expect to be present (like here) has actually a meaning of future tense.
Yes, it is the perfective of "mówić". Usually the perfective/imperfective pairs are very similar words, but not always, as you can see.
"oni" = there is at least one man among 'them'.
"one" = there are no men among them. So generally women/girls only, although theoretically any other plural word could also be put here.
Are pronouns preferred in the 3rd person? Could you just say ,,Mówią, że słyszą głosy"?
They are for sure more probable, but still, the subject is probably known from the context so the pronoun is still redundant. Yes, you can say that.