Did the father break his oath of divorce after giving his paternal aunt food and drink, despite swearing that he would not give her money, and can he give her money later without the divorce occurring?

A Muslim is not permitted to swear by other than Allah. The prohibition is even stronger regarding oaths of divorce, as they are oaths of the wicked. A conditional divorce takes effect upon the fulfillment of the condition. If your father did not do what he conditioned the divorce upon, which was giving money to your aunt, then he does not break his oath if he gives her something other than money. However, if he gives her the money, then he does break his oath. There is no way to dissolve an oath after it has been made except by breaking it.