What is the nature of the blood that descended on September 15th, is it considered menstruation or istihadha (non-menstrual vaginal bleeding), what is the reason for its descent, and what is the ruling on circumambulation (Tawaf) and prayer while it is descending?

Your Hajj is valid - God willing - whether the blood was menstruation (hayd) or irregular bleeding (istihada). If it was menstruation and you performed the circumambulation of Ifadah (Tawaf al-Ifadah), then you are not required to perform the circumambulation of farewell (Tawaf al-Wada'), and your Hajj is complete. If it was irregular bleeding, then there is no issue, as you performed the circumambulation of farewell. To determine whether the blood is menstruation or irregular bleeding, it depends on whether it occurred during a time suitable for menstruation. If the previous menstruation had ceased at least thirteen days before you saw this blood, and this recurring blood did not last more than fifteen days, then it is menstruation. However, if you saw it before thirteen days had passed since the cessation of the previous blood, or its duration, including any intervening periods of purity, exceeded fifteen days, then you are experiencing irregular bleeding.