Are the children whom their father specified to receive apartments during his lifetime, but who did not take possession of them until after his death, entitled to these apartments, or are they considered part of the estate to be divided among all heirs?

Parents must be just in giving gifts to their children; it is not permissible to favor some over others. If a father favors some of his children and then dies, the one who was favored must return what they took to the estate so that it can be divided among all heirs according to the Sharia-compliant distribution. If the heirs refuse this solution, then everything that was gifted must be returned to the estate and divided among the heirs according to each heir's share.