Is it necessary to make up for the fasting and repeat the prayers after discovering a transparent film on the nail that might have prevented water from reaching it, subsequent to a period of prayer and fasting?

Everything that prevents water from reaching the skin during ablution (Wudu') and ritual bathing (Ghusl) must be removed. If the crust acts as a barrier, it must be removed, for the original principle is that a barrier prevents water from reaching [the skin] unless proven otherwise. Therefore, if in doubt, one must repeat the ablution and the prayer. As for fasting, it remains valid and is not related to any error in ritual purity.