Is it necessary to wash the entire garment or wash one's hands after washing a spot of impurity if the water exceeds the boundaries of the spot, with no trace of the impurity remaining?

It is not obligatory to wash the entire pair of trousers if only a part of it becomes impure; rather, it suffices to wash only the impure spot. Water reaching other areas does not necessitate washing the entire pair of trousers. If your hands are not impure, you are not obligated to wash them. The water remaining on the trousers after the impurity has been removed is pure, and it is not obligatory to wash the hands from its residue.