Must one pray if there is pain and bleeding after the usual menstrual period has ended, or is the woman still considered to be menstruating even after the original time of her period?

If the blood continues for more than fifteen consecutive days, then you are experiencing استِحاضة (istihadah - irregular vaginal bleeding outside of menstruation). In this case:

1. Reverting to previous habits: Consider what aligned with your previous habit as menstruation, and anything beyond that as istihadah. 2. Discernment: If you do not have a previous habit, then distinguish menstrual blood by its characteristics (color, odor, and accompanying pain), and consider what possesses these characteristics as menstruation, and anything else as istihadah. 3. After the menstrual days have ended: Perform ghusl (ritual bath), pray, and do what pure women do. 4. Ablution for prayer: Perform wudu (ablution) for each prayer after its time has begun, and pray with this wudu as many obligatory and supererogatory prayers as you wish. 5. Protection: Use a cloth or similar item to prevent the spread of impurity.