Is it permissible to throw the Jamarat after midnight on the Day of Departure (Yawm al-Ta'ajjul), and then perform the Farewell Tawaf and depart from Makkah? And what are the consequences of doing so?

If hurrying in throwing the pebbles means throwing the last day's pebbles after midnight, then this throwing is not valid and necessitates a sacrifice (dam) to be slaughtered in Mecca and distributed among the poor of the Haram.

As for sleeping after the farewell circumambulation (Tawaf al-Wada'), if it was performed earlier intentionally for the purpose of sleeping afterwards, then it must be repeated or a sacrifice (dam) must be offered. But if the delay was due to circumstances beyond one's control, then repetition is not necessary.