What should a woman do if her postpartum bleeding (nifas) stops after 40 days, but then her menstrual period continues longer than usual, with light spotting at night after the bleeding has stopped during the day? And in this situation, is she required to perform ghusl and pray?

The blood you saw for eight days is considered menses if it did not exceed 15 days. If it stopped and you saw purity, you must perform ghusl (ritual bath) and pray. If the blood returns, you are considered in menses again and must perform ghusl again after it stops, as long as the total duration of blood and purity does not exceed 15 days. If the duration exceeds 15 days, then you are experiencing istiḥāḍah (non-menstrual vaginal bleeding). The purity interspersed with blood is valid purity during which your acts of worship are sound.