Is a man religiously required to pay a sum of money to his former wife as compensation for emotional harm, based on a court ruling, or is he not religiously required to do so?

A father is obligated to provide for his daughter. As for the wife's maintenance, he is not obligated to provide it except during the waiting period (iddah) if the divorce is revocable (raji). Once the iddah period ends, the maintenance obligation is legally waived. Moral damages do not necessitate him paying compensation, and he is permitted to find a way around an unjust ruling and reject it, provided it does not expose him to greater harm.