Does a divorce take place when the husband says to his wife, "You are divorced," after she asks, "Do you want a divorce?" and she replies with "Yes," and what is the ruling on reconciliation (rajʿah) and the waiting period (ʿiddah) in this case?

If you uttered a clear divorce statement while being aware, then the divorce has occurred, even if it was during a state of intense anger that did not completely impair your intellect. If this pronouncement does not complete three divorces, then you may reconcile with your wife before the expiration of her waiting period (iddah (definition)). We caution that anger is the key to evil, and the Prophet, peace and blessings be upon him, advised against anger.