Why "nie musze mowic" is wrong?
I think duolingo got stuck with Polish clear distinguish between mówić and rozmawiać.
But I can imagine situation where English "I do not have to talk." is Polish "nie muszę mówić".
"Nie muszę mówić" is accepted as well.
Why not "Nie muszę porozmawiać"
As "porozmawiać" means "to have a conversation", I don't think you can use it without mentioning talking "to/with whom" part. Especially that it's a perfective verb.