Do the six properties count as part of the inheritance despite the mother gifting some of them to certain heirs, what is the ruling on the action of the son who sold the property gifted to him, and must the two brothers repay the amounts withdrawn from the joint account before the mother's death so that they are included in the inheritance?

It is not permissible for parents to favor some children over others in gift-giving unless there is a legitimate Sharia (definition)-compliant reason. If the father dies having made such a preference, the favored child must return the gift to the estate, or it will be deducted from his share. If the child sold the favored property while being poor and in need, it will not be counted against him; otherwise, it will be deducted from his share. The same applies to money withdrawn from the account: if it was for a need and with the mother's consent, it will not be counted; otherwise, it will be deducted from their share.