Does Islamic law approve of a father's actions when he favors some of his children in spending and gifts, and tries to conceal that, and does Islamic law permit him to transfer ownership of his properties to his second wife through a fictitious sale, and what is the impact of that on the affection among the children?

There is no harm in a man marrying a woman younger than him, and polygyny is not an injustice to the first wife. However, there must be justice between wives in lodging and maintenance. Similarly, there must be justice between children in gifts and endowments, and favoring some over others is an injustice and invalid. A father writing his property in his wife's name is not considered a valid sale but rather a bequest to an heir, which is not valid unless the other heirs consent. The father must repent and be just, and the children must advise him gently and kindly. If he does not respond, they must still honor him and not be disobedient.