After the cessation of postpartum bleeding (nifas) and the insertion of an IUD, and the subsequent return of bleeding, is fasting and prayer obligatory?

The default assumption for blood discharged by a woman is that it is menstrual blood, unless it exceeds 15 days. The menstrual period may increase, decrease, come earlier, or be delayed, and the blood discharged in these cases is considered menses. The insertion of an IUD causes disturbance in the menstrual cycle. The blood you are experiencing is considered menstrual blood, unless it exceeds 15 days, in which case you become a woman experiencing Istihadah (prolonged non-menstrual vaginal bleeding). If it is confirmed that you are experiencing Istihadah, then you should either rely on your previous habit (of menstruation), or distinguish between thick, black blood with a foul odor (menses) and light, thin blood (Istihadah), or you observe six or seven days (as menses) then perform ghusl (ritual bath) and pray. A woman experiencing Istihadah fasts, prays, and may have marital relations, and she performs Wudu' (ablution) for each obligatory prayer after its time has entered.