Will the prayer rug be purified by wiping the madhy (pre-seminal fluid) with a wet tissue if the tissue dries on it? Will the corners of the house become impure by stepping on the spot with a wet foot? Do those who prayed on the rug and the residents of the house have to repeat their prayers?

Purifying a hand that has become impure (najis) is done by washing it with water, not by wiping it with a wet tissue. If an impure hand is wiped with a tissue, it does not become pure by that action, and the tissue becomes impure. If the impure tissue is placed on a prayer rug (sajjadah), then if one is not certain that the impure part of the tissue touched the rug, the rug is not ruled to be impure. However, if one is certain of the contact, there is a difference of opinion among scholars regarding the transfer of impurity. The most preponderant view is that if a wet impure substance touches a pure substance that is not wet to the extent that if squeezed, nothing would drip from it, then the pure substance does not become impure. Accordingly, there might be leniency in the non-transfer of impurity, but it is better to wash the spot that is certainly known to have been touched by the impurity.