What is the criterion for dryness of the hand, and when is a hand judged to be dry such that impurity is not transferred by its touching another dry thing, given that the hand has natural moisture or dampness or slight perspiration? And what is the ruling on using soap that contains pork fats or fats from animals not slaughtered according to Islamic law, and is its impurity dependent on a chemical transformation of the substance?

The treatment for someone suffering from waswasah (obsessive whispering/doubts) is to avoid mentioning detailed jurisprudential branches, as these only increase the waswasah. Engaging extensively with someone suffering from waswasah only increases their waswasah, especially if their problems contradict what rational people agree upon. The hand is originally dry and does not have natural moisture, as the questioner claimed. What jurists mean by moisture is that the item has wetness or dampness. Therefore, the person suffering from waswasah must ignore the moisture or wetness that they imagine on the hand, and proceed on the basis that it is originally dry, and dry impurity does not transfer to it if it comes into contact.

As for soap proven to contain impurity from an unslaughtered animal, this does not prevent its use when needed, because direct contact with impurity due to necessity is permissible according to many jurists. The user of the soap will wash their hands with water afterwards. Sheikh al-Islam Ibn Taymiyyah mentioned that medical treatment involving smearing with impurity and then washing it off is permissible when needed.