Is blood due from me because of staying the night of Tuesday after performing the farewell circumambulation on Monday, knowing that my departure was at dawn on Tuesday?

If you stayed for the aforementioned period after the Farewell Tawaf, knowing that your departure was delayed, and it was possible to delay the Farewell Tawaf, then you are obligated to repeat it. In this case, you are like one who omitted it, and a dam (sacrificing a sheep in the Haram and distributing it to the poor) is incumbent upon you.

According to the Hanafis, the time for the Farewell Tawaf extends after the Tawaf al-Ziyarah, and any circumambulation performed by the pilgrim after the Tawaf al-Ziyarah suffices for the Farewell Tawaf. They do not stipulate immediate departure after the Tawaf.

However, according to the Malikis, Shafi'is, and Hanbalis, the time for the Farewell Tawaf is after completing all matters and intending to depart. Only being occupied with matters related to travel afterward is excused. If one becomes occupied with something else unrelated to travel matters, then repeating the Tawaf becomes incumbent upon them.