What is the ruling on shaking hands with someone whose hand is sweaty, and a dog may have licked it, and is the hand considered ritually impure (najis) and must be washed, and does the ruling transfer to everything the hand touches? And what are the guidelines for the transfer of ritual impurity from a dog or other sources?

The default state of the hand of someone you shake is purity. There is no need for excessive scrutiny and overthinking that leads to waswasa (obsessive doubts), as the scholar Al-Uthaymeen, may Allah have mercy on him, said: "Certainty dictates that this ground or this rug is pure. If a person doubts whether it has been touched by impurity or not, it does not become impure; rather, it is pure by ruling." He also mentioned the hadith: "He should not leave - meaning the mosque - until he hears a sound or finds a smell."

The default state is that your hand and whatever you touch with it are pure. The rule for the transfer of impurity is as follows: If the impurity is dry, and a pure, dry object touches it, the impurity does not transfer. If it is wet, it will render impure any dry, pure object it touches. If the impurity is dry and a pure, wet, or moist object touches it, then the impurity transfers to it.