Does a wet foot become impure if it touches a dry impure spot on a carpet, and does the foot become impure if it touches a spot that was thought to have been purified with a cleaning liquid, but then there was doubt about walking on it after pouring water?

Semen is pure according to the most preponderant opinion of scholars. The default state of things is purity, so unless certainty of impurity transfer is achieved, the original state remains presumed. If a wet foot treads on a prayer rug, it does not become impure unless you are certain that it stepped directly on the spot of impurity itself. Assuming a wet foot does step on a dry impure spot, there is a difference of opinion regarding the transfer of impurity from a dry impure object to a wet pure one. It is permissible to adopt the view that impurity does not transfer due to hardship, and because a person afflicted with waswas (obsessive whisperings) is permitted to adopt the easiest opinions. We advise you to turn away from these waswas and not to indulge them.