Is the bleeding that occurs after the insertion of an IUD considered menstrual blood or irregular bleeding (istihada), given that its discharge began after purification from the usual menstruation on the sixth day, and the typical menstrual period is seven days? Does this entail making up prayers and fasting, and abstaining from intercourse?

If the blood stops after the IUD insertion and then returns during the regular period, it is considered menstrual blood (hayd), and one must cease fasting and prayer. As for the blood that appears after the usual period ends, it is also considered hayd, as long as its total duration does not exceed 15 days. If it exceeds 15 days, then it is considered irregular bleeding (istihada), and purification and ablution are required for each prayer. For the days exceeding your original habit, you must make up the prayers you missed during them. As for intercourse that occurred during this period, there is no sin in it due to the assumption that it was istihada. The preponderant opinion is that a change in the habit, whether by increase or decrease, is hayd as long as the duration does not exceed 15 days; if it exceeds that, it becomes istihada.