How is the ruling of impurity transferred? Does this include all types of visible and invisible impurities, and various liquids such as creams? Is impurity transferred to a sweaty hand or socks wet with sweat after touching the impurity and then drying?

There is no difference between wet and moist in the ruling concerning impurities (najasa). Dry impurity does not transfer to something dry like it. However, wet impurity transfers whether it encounters a wet or dry place. Liquids are affected by impurities, and impurity transfers through them. There is no difference between visible and invisible impurity if its contamination of a place is known. However, a small amount of impurity that cannot be perceived by the eye is excused due to the difficulty of guarding against it. The Sunnah is to promptly remove impurity without leaving it to dry. If impure feet sweat, the impurity transfers to the socks.