Are the children considered his children legally, and do they inherit from him, and are they considered mahram to their paternal aunts, given the hadith that prohibits attributing a child to anyone other than his father? And is it obligatory to inform the wife about the knowledge of her husband's infidelity, and what happens after repentance?

The child is attributed to the husband who owns the bed [i.e., the husband of the mother], and this entails the establishment of ḥurmah (prohibition of marriage), maḥramiyyah (being a unmarriageable kin), inheritance, and everything related to lineage. The ḥadīth: "Any woman who introduces into a people a lineage that is not from them, then she is not from Allah in anything," pertains to the ruling in the afterlife and does not contradict the attribution of the child to the bed, as long as the husband does not deny it through liʿān (oath of condemnation). The husband should continue with his wife if she repents, and beware of denying his children, due to the punishment for slander that results from it. It is advised to teach his wife matters of her religion and connect her with righteous women.