Is the blood discharged on the fifteenth day after the first menstruation considered menstruation, and is ghusl (ritual bathing) and a repeat of the fast obligatory thereafter? Is the fasting of the days that followed the first menstruation and preceded the discharge of the second blood valid? And are the prayers and fasting of the days that followed the ghusl from the first menstruation and preceded the discharge of blood on the eleventh day, which was confirmed not to be menstruation, valid?

The returning blood in both months is menstruation because it occurred during a time when it could be menstruation. Ghusl (definition) (ritual bath) becomes obligatory after its cessation, provided that its total duration, combined with the preceding blood and the interval between them, does not exceed 15 days. If you did not perform ghusl after seeing the returning blood in the previous menstrual period, you have made a mistake. There is a difference of opinion regarding the obligation to repeat the prayers you performed without ghusl. However, the acts of worship performed during the intervening period of purity are valid.