If a husband tells his wife, "You are forbidden to me in this world and the Hereafter," intending thereby to forbid intimate relations, after they have reconciled, does this make her unlawful to him, and is it permissible for him to resume marital relations with her again?

Prohibiting one's wife has details; it could be a divorce, or a ẓihār, or an oath, depending on the husband's intention. If he intended to refrain from intercourse with her, then it is considered an oath, and he is bound by an expiation for an oath (kaffārat yamīn) if he has intercourse with her. The expiation for an oath is feeding ten poor persons, or clothing them, or fasting three days for whoever is unable to do that.