What is the ruling on ghusl and what is the ruling on the prayers performed if a cotton swab was not used to confirm purity after the cessation of bleeding and seeing dryness for hours, and then a brownish discharge appeared thereafter?

Purity from menstruation is recognized by one of two signs: the emission of a white discharge (al-qassah al-bayda'), or complete dryness such that the cotton swab comes out clean. Not seeing blood on clothes is insufficient, as blood might still be inside the vagina. If you performed ghusl (definition) based on the absence of blood, and then a brownish discharge appeared, the ghusl is valid if the preceding cessation had removed the blood. However, in the future, you must ensure purity by inserting a cotton swab before performing ghusl.