What is the ruling on constant doubt regarding a wife's betrayal, and does it lead to divorce or prohibition (of her)? And what is the ruling on forgiving a wife after being certain of her betrayal?

The wife is not divorced, nor does she become unlawful to her husband, merely by suspicion of her adultery. Even if the husband becomes certain of her adultery, this does not affect the validity of the marriage. However, it is unlawful for him to condone her in such an act. The default state for a Muslim is innocence, and whoever accuses them otherwise must provide proof or face the punishment for slander. It is not permissible to spy on a Muslim. Nevertheless, the husband must not leave his wife to do as she pleases; rather, he must ascertain the matter. If he becomes certain of adultery, then he should know that Paradise is forbidden for the cuckold (dayyūth).