Is the statement that says if a ritually impure garment is squeezed and no drops fall from it, and then it is wrapped in a dry, pure garment, its moisture does not contaminate the pure garment, correct? And does this ruling apply to pre-seminal fluid (madhy) on clothes?

What you have read from the Hanafi school of thought is correct: a pure garment does not become impure if it is touched by dampness due to being wrapped in a wet, impure garment that cannot be wrung out, because no part of the substance of the impurity separates from it. This is in contrast to a garment wet with impurity, such as urine; if it touches a garment or body and dampness separates from it, then it must be washed, because that dampness is the impurity itself. It is advised to turn away from obsessive doubts and not pay attention to them.