Is it permissible to perform Hajj on behalf of a deceased person for a sum of money, and is it permissible to repeat Hajj on their behalf in the same manner?

There is no objection to appointing someone to perform Hajj on behalf of the deceased for a fee, whether the Hajj was obligatory or voluntary, and the permission of the deceased is not a condition. It is required that the proxy must have already performed Hajj for himself first. It suffices for him to enter into the state of ihram from his own miqat, not from the miqat of the deceased's people.