Does a divorce take place if a husband says to his wife, "You are divorced... you are divorced," twice in a moment of anger, without intending divorce, and then they reconcile and he takes her back by saying, "I have returned you to my marital bond"? Is it a condition for divorce to take place that there be witnesses?

If you utter the explicit words of divorce, being aware of what you are saying, and acting voluntarily without coercion, then your divorce has taken effect, even if you were extremely angry, and even if you did not intend divorce.

If you repeat the words of divorce for emphasis, and not to initiate another divorce, then only one divorce occurs.

It is not a condition for divorce to take effect that there witnesses to it.

If this divorce is not the completion of three divorces, and you reconcile with your wife before the expiration of her waiting period (iddah), then the reconciliation is valid and occurs without witnesses according to the majority of scholars, though it is recommended to have witnesses to it.