Do the procedures that took place between the spouses count as a divorce, knowing that the husband did not utter the divorce and had no intention of saying it, and he divorced her in the divorce document with a revocable divorce?

If you authorized your friend to finalize the divorce proceedings, then the divorce is apparently effective, even if you did not utter the words yourself. The Egyptian Dar al-Ifta has issued a fatwa stating that divorce takes effect merely by the husband's order to write the divorce deed, and that if the ma'dhun (authorized officiant) writes the document based on this order, it is considered a divorce by consensus. Since the divorce is revocable, the wife can be taken back before the expiry of her iddah (waiting period).