Is the blood that flows after the insertion of the IUD subsequent to postpartum bleeding considered irregular bleeding (istihada), which necessitates prayer and fasting despite it flowing onto the thighs?

Brown discharge before blood is considered menses if it occurs within the customary period, but not otherwise. Blood is considered menses as long as it does not exceed 15 days; if it exceeds that, then you are experiencing istihaadah (non-menstrual vaginal bleeding). A woman experiencing istihaadah should refer to her customary period. If she does not have a customary period, then she should differentiate between menstrual blood and istihaadah based on the characteristics of the blood. If she has neither a customary period nor the ability to differentiate, then she should consider the prevalent custom among women (six or seven days), then perform ghusl (definition) and make wudu for every prayer after its time has begun, taking precautions.