Is it permissible for someone performing 'Umrah to do so on behalf of an infant wearing diapers, and is it permissible for the infant's mother to wear a baby carrier (sheyala) to carry him during 'Umrah?

If the questioner intends the ihram for a child, then the child is prohibited from what an adult is prohibited from, such as sewn clothes, and this includes diapers, unless there is a necessity. In such a case, the fidyah (expiation) is incumbent upon the child's guardian, which is fasting for three days, or feeding six poor people, or sacrificing a sheep. As for baby carriers, there is no harm in them, because they are not clothing.