Is it sufficient to merely wash a ritually impure hand that has a wound, without rubbing the wound itself? And if I wash the hand and doubt the purity of the water, does the wound water become impure, and must the hand be rewashed?

Pus, discharge, and the fluid that emerges from wounds are considered impure by the majority of scholars, though some jurists deem them pure. A small amount of impurity is pardoned. As for those who suffer from obsessive doubts (waswasah), they may adopt the view of those who consider it pure and disregard their doubts.