Is wiping away a child's impurity with a perfumed wipe sufficient to remove the impurity, and does the ruling on an unperfumed wet wipe differ from that of a perfumed wipe in removing impurity, and does the bedding become impure by wiping a child's impurity with a perfumed wipe and then placing it upon the bedding?

The place of impurity is not purified by wiping it with wet wipes; rather, the spot must be washed with water. There is no fatwa (definition) that permits the use of scented wipes to purify a place of impurity. They are only for removing the impurity from a child, not for purification, because a child does not need what an adult needs.

If you do not know that impurity has soiled the bedding, then the original state is purity, and certainty is not removed by doubt. But if you know that impurity has soiled the bedding, then it is purified by washing the impure spot with pure water.