Does a divorce issued with the intention of calming the situation and removing harm, and in a state of extreme anger resulting from the wife's provocation and physical assault by pulling hair, and repeated demands for divorce, take effect?

If the anger is so severe as to lead to a loss of awareness when uttering a divorce, then it does not take effect. It is advised that both spouses fear Allah, live together amicably, show understanding and compassion, and avoid anger, as it is the key to evil, as stated in the prophetic tradition: "Do not get angry."