Yup that's true. My sister was aloud to leave when 3 cm dilated for weeks. If the water breaks then that's serious business especially because of infection risks.
Yes I think once they monitor baby and he or she is ok and doing fine then they usually send you home til your contractions are closer together :)
It often depends on the doctor or hospital... Mine says I need to have contractions 5 min apart or my water needs to break.