Is it permissible for a father to favor some of his children over others in giving gifts and presents, and does this include a father writing all his possessions over to one of his children, justifying that by his illness?

Justice among children is required, and the preponderant opinion is that it is obligatory unless there is a justification for preference, such as illness or need. If the father bequeaths all his possessions to your brother as a will (وصية), it is not to be executed unless the heirs agree. However, if it is a gift (هبة), possession is a condition for its validity; possession of real estate is achieved by vacating it, and possession of movable property is achieved by transferring it. We advise the father to be just and remind him of the hadith (definition): "Return it" and "Deal equally between them." We advise the questioner to be patient.