Is fasting and praying obligatory when there are intermittent black discharges after the usual days of menstruation have ended, knowing that these discharges only appear upon entering the restroom?

If the discharge is blood, it is menses as long as its duration does not exceed fifteen days. Fasting or prayer is not permissible while it is present, and those days must be made up after Ramadan (definition).

As for yellowish or brownish discharge: - If it occurs during the usual period or is connected to blood, its ruling is that of menses. It prevents fasting and prayer, and those days must be made up. - If it appears after the end of the usual period and seeing purity, it is not considered menses and does not prevent fasting or prayer. One must cleanse oneself from it, wash what has stained the clothes, and perform ablution.