Is it obligatory to fast and pray two or three days after the cessation of menstruation, or after the appearance of the sign of purity after six days?

If the heavy bleeding stops but its color remains, then you are in menstruation (hayd) and must await either the "white discharge" (al-qassah al-bayda') or complete dryness of the vaginal area. You are not obligated to pray or fast at that time. However, if the blood stops completely and the cloth inserted into the vagina becomes dry, then this is a valid purification (tahara shar'iyya), and there is no need to wait for six days.