Is it obligatory to re-fast Thursday, Friday, and Saturday for someone who performed ghusl at dawn on Thursday after her menses stopped on Wednesday, and did not see the white discharge but rather a light yellowish discharge resembling daily secretions, then saw a yellowish discharge again after Maghrib and performed ghusl as a precaution, then saw a very small yellowish spot on Friday afternoon, knowing that her menstrual cycle usually lasts seven days?

A woman knows she is pure by one of two signs: dryness or the white discharge. Yellowish and brownish discharges connected to blood are considered menstruation. However, if they are not connected to blood, they are not considered menstruation unless they occur within the usual period. Since your usual period is seven days, the yellowish discharge you saw after your first ghusl (ritual bath) and after Friday afternoon prayer is not considered menstruation. Your acts of worship during that period are valid, and you are not required to make up for any of them.