What is the ruling on a husband taking his wife back after he uttered to her: "You are divorced, divorced, divorced, and by God, you will not remain married to me"? And is this wording considered one divorce or three divorces?

If a man says to his wife: "You are divorced, divorced, divorced," and he intended one divorce or did not intend anything, then only one divorce is binding upon him. If he intended three divorces, then three are binding upon him according to the majority of scholars, and a major irrevocable divorce (baynunah kubra) occurs. She does not become lawful for him until she marries another husband. However, if only one divorce was binding upon him, he may take his wife back before the expiry of her 'iddah (waiting period).

As for his statement: "By Allah, you will not remain under my marital bond," this is an oath by Allah. Breaking it depends on his intention. If he takes her back, and he intended not to take her back, he has broken his oath and an expiation for breaking an oath becomes obligatory upon him.