How does a woman handle her prayers and fasting if her menstrual period lasts for more than three months, with brown and gray discharge, and is the occurrence of this discharge considered normal with irregular periods, and is it permissible for her to place a sanitary pad and pray with it without changing it, while renewing her ablution?

The duration of menstruation is the period of known red blood. If this period ends and yellowness appears, then perform ghusl and pray. Your ruling for the rest of the month is that of a woman experiencing istihada (non-menstrual vaginal bleeding). You may adopt the view of the Malikis that continuous yellow or brownish discharge does not invalidate ablution, because their madhhab is that continuous discharge does not invalidate ablution. Taking precautions to prevent the spread of impurity is better, but if it becomes difficult for you, there is no sin in omitting it.