Are the white or black substances that accumulate under the nails after showering impure, given that they result from dry sweat mixing with impurities on the bed? And does the dirt around the nipple prevent water from reaching the skin?

The dirt clinging to the body or clothes due to dust, sweat, etc., is pure, and the basic principle regarding things is purity. Some scholars are of the view that a slight barrier is excused. As for madhy (pre-seminal fluid), it is impure. If you are certain that it has touched your body, its location must be washed. If it is merely a doubt or a whisper, then the basic principle is the purity of the body, and its impurity is not ruled upon except with certainty.