If I remember correctly from school, in general Polish interpunction is working a lot like German, so all sub-clauses of a compound sentence should be divided with comma, with the exception of "albo", "lub", "czy", "bądź", "i", "oraz" and "ani"(maybe a few others conjunctions too, not sure); for sure, all dependant clauses should be separated by comma.
Anyway, I think that "że" is not a general rule but a 100% rule – I don't remember any exception for a lone standing "że", through there might be exceptions when it is connected with something else(certain prepositions, IIRC) or part of the compound("także", IIRC, doesn't force comma). But that's just a guess – I'm dreadful with interpunction in general. ;-)
"mówić" focuses on the process of speaking, "powiedzieć" focuses on conveying the message. "mówić" can translate to speak/say/tell, "powiedzieć" to "say" or "tell" (in the past/future, as it's perfective, it cannot be used in present tense).
Ona mówiła przez trzy godziny. = She was talking for three hours
Ona powiedziała, że... = She said that...