Is it permissible for a pilgrim to depart from Muzdalifah before midnight to stone Jamrat Al-Aqaba (the Great Jamrah), especially when there are active women present, and what are the implications of that?

Staying overnight in Muzdalifah is obligatory. It is not permissible for the pilgrim to depart from it to Mina before midnight. The best is to depart after Fajr. Whoever departs before midnight must offer a sheep to be slaughtered in Mecca and distributed among the poor of the Haram. And whoever stones the Jamrat al-Aqabah before midnight on the night of sacrifice must offer another sacrifice.