Is ghusl obligatory and is the fast acceptable if a small amount of blood mixed with clear white discharge or brown blood is discharged during the ovulation period for an unmarried woman?

If the blood is considered menses (not less than one day and one night, and not exceeding 15 days), then ghusl (definition) is obligatory after its cessation, and you must make up the day on which you saw the blood. The Maliki school of thought does not specify a minimum for menstruation, and according to their view, ghusl and making up the fast are incumbent upon you, which is the more cautious approach. As for brown discharges (al-Kudrah), if they are considered menses, then ghusl is obligatory, and you must make up the days on which you fasted while experiencing them; otherwise, not.