What is the ruling on prayer if a woman had a miscarriage, then menstruated and became pure, and after a week, her period returned with heavy, incessant bleeding, bearing in mind that the second menstruation might not be considered menstruation until 15 days after purity?

If the miscarriage occurs before 81 days of pregnancy, the blood is considered istihada (irregular bleeding). You should count as menstruation what corresponds to your usual period, or what you can distinguish as having the characteristics of menstrual blood. If you do not have a habit nor can you distinguish, then you should consider six or seven days by estimation, and perform ghusl (ritual bath) after the completion of the menstrual period. Then, you should perform wudu (ablution) for each prayer, and you are considered pure.

However, if the miscarriage occurs after the formation of the fetus and after 81 days, the blood is considered nifas (postnatal bleeding). What falls within the forty-day period is nifas, and what exceeds it is istihada, unless it coincides with the time of your usual period.