What is the ruling on swearing "your mother is unlawful to me" if the son returns to what his father swore he wouldn't, and what is the ruling on swearing by divorce if the wife responds to her paternal aunt's wife's question with the intention of helping? And in both cases, does it constitute a divorce or not, and how is expiation paid?

The ruling on whether your father has broken his oath or not depends on his intention at the time of swearing the oath, because intention specifies the general and restricts the absolute.

In the first oath: If he intended to prevent your mother from speaking to your uncle's wife absolutely, then he has broken his oath by her speaking to her, and divorce has occurred, unless he did not intend divorce but merely intended prevention, in which case he must offer expiation for breaking an oath (kaffarat yamin). However, if he intended to prevent her from speaking to her in a specific manner without preventing her from responding to her question, then he has not broken his oath.

In the second oath: If he intended to delete the games and not restore them, then he has broken his oath by the child reloading the games. If he did not intend that, then he has fulfilled his oath. In the event of breaking the oath, one refers to his intention regarding what he meant by the prohibition: if he intended divorce by it, then it is a divorce; if he intended ẓihār (a form of divorce by injurious assimilation), then it is ẓihār; and if he intended an oath or did not intend anything specific, then it is an oath like the expiation for breaking an oath.

Therefore, it is advised to present the matter to trustworthy scholars in the questioner's country due to the details and differences of opinion among scholars.