What is the ruling regarding a wife who sees menstrual blood for more than two consecutive months due to her taking birth control pills, which causes her confusion in performing prayers and reading the Quran?

Your wife is experiencing Istihadah (prolonged vaginal bleeding outside of menstruation). She must refer to her previous regular menstrual cycle. If not, then she should differentiate between menstrual blood and other blood (Tamyiz). If that is also not possible, then she should consider herself menstruating for the prevalent duration of menses, which is six or seven days. After the menstrual period ends, she performs Ghusl (ritual purification), prays, fasts, and all rulings applicable to ritually pure women apply to her. Intercourse is permissible with her. However, she must perform Wudu (ablution) for every prayer after its time has begun, and she prays both the obligatory and supererogatory prayers until the time for that prayer exits, while taking precautions by tying a cloth over the area.