Must the major ritual bath be repeated and the fasting of Ashura be invalid, if the presence of nail polish that prevents water from reaching [the skin] is discovered after bathing and sleeping?

If you find an obstruction that prevents water from reaching a spot during ghusl, remove it and wash that spot only. You are not required to repeat the entire ghusl, as continuity (muwalat) is not a condition for the validity of ghusl according to the majority of scholars. However, if you have prayed any of the prayers with this incomplete ghusl, you must repeat them. As for the fast of Ashura, it is valid, because purity is not a condition for the validity of fasting.