Does the hand become impure when washing the male organ with water without seeing any impurity on it? And is it permissible to insert the impure hand into a bucket to wash it if the water in the bucket does not change?

The hand becomes impure if it is touched by urine or by water that has separated from an impurity (whether the water has changed due to the impurity or not, before the impurity is removed). It must be washed before being put into a vessel to avoid rendering the water within it impure, because a small amount of water becomes impure upon contact with impurity according to the majority of scholars. If the hand becomes impure, it must be washed outside the bucket to avoid rendering the water inside it impure, and this is the view of the majority of scholars.