Is it necessary to repeat the fast, prayer, and ghusl if ablution was performed while there was peeling dead skin on the feet that was not removed until later?

The skin on the sole of the foot is not dead scaly skin that must be removed. Rather, it is firm skin connected to the body. The validity of wudu (ablution) and ghusl (ritual bath) is not affected by its presence as long as it is attached to the body. Therefore, there is no need to repeat the prayers. As for fasting, purity is not a condition for it at all. We advise against excessive scrupulousness in matters of purity and to beware of obsessive doubts (waswas).