Is doubting a wife's deletion of calls and messages considered an accusation of unchastity (qadhf)? Is the husband sinful and required to offer expiation for that? And what is the ruling on his taking a false oath (yamin ghamus) to her brother that he did not call her "O traitor," when in fact he did?

What the questioner said is not slander. It is not permissible for the husband to harbor ill-will towards his wife without proof, for Allah Almighty says: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." If there is no suspicion that calls for doubt, then he must repent. As for the "yameen al-ghamūs" (a false oath sworn deliberately to usurp another's right), it is a grave offense and one must repent from it.