Does dry impurity transfer from the hand to something else, and does it continue to transfer indefinitely even if no trace of it appears after several transfers?

It was previously explained that if something impure meets something pure and both are dry, it does not contaminate it. However, if something wet meets something that has become impure, it becomes impure. For example, a sweaty hand that touches something impure from urine that is dry will become impure according to the Shafi'i and Hanbali schools, but not according to the Hanafi and Maliki schools. Impurity does not become pure by drying but by remaining. So, if we are certain of its presence, we rule that whatever it touches becomes impure, unless it is dry. If we doubt its presence, we do not rule that whatever it touches becomes impure.

The questioner, who suffers from obsessive doubts (waswas), is advised to disregard them.