What is the ruling on the fast of one who experiences bleeding after her menstrual period, and is ghusl required of her?

This blood that you see on the thirteenth day after your period is not considered menstruation (hayd); rather, it is irregular bleeding (istihadah (definition)), which does not prevent prayer or other acts of worship. This is based on the Maliki view that the minimum period of purity (tuhr) between two menstrual cycles is fifteen days, a view held by Ibn Maslamah and popularized by a group of shaykhs. We advise you to ask a scholar in your country and act according to their fatwa (definition).