Are the six days exceeding the usual duration of menstruation considered istihadah (post-menstrual bleeding), and what is the ruling on performing Tawaf and Umrah during this period?

The maximum duration of menstruation according to the majority of scholars is fifteen days and nights. If bleeding exceeds the usual duration but does not exceed 15 days, it is considered menstruation. Based on this, your assumption of ihram for the second 'Umrah was valid, but your circumambulation (tawaf) while menstruating was not valid. This is because the majority of scholars hold that a menstruating woman is not permitted to perform tawaf, due to the Prophet's (peace be upon him) saying to 'A'ishah: "Do everything a pilgrim does, except circumambulate the House until you become pure."

Therefore, you are still in a state of ihram and must refrain from what a muhrim (person in ihram) refrains from. Then, you must return to Makkah to complete the tawaf of 'Umrah and the sa'y (as your first sa'y was not valid), and then you may exit ihram.

If you are unable to go to Makkah, your ruling is that of a person prevented from continuing (muhsar): you must slaughter a sacrificial animal (hady). If you are unable to do so, then you must fast for ten days. This is based on the view that blood exceeding the usual duration is menstruation, even if it does not recur. However, for those who stipulate recurrence (like the Hanbali school), this blood is considered istihada (non-menstrual bleeding), and what you did is valid. The more cautious approach is the first opinion.