Do the first and second divorces count as a single divorce so long as the husband has not reconciled with his wife after the first divorce? And is his wife forbidden to him after the third divorce, while he regrets divorcing her, and she is pregnant and has children from him?

If the second pronouncement of divorce (talaq) occurs before the expiry of the waiting period (iddah) of a revocable divorce, it is effective according to the majority of scholars, in contrast to Ibn Taymiyyah, who holds that it does not take effect. If the waiting period expires before reconciliation (raj'ah), then you become a stranger to him, and the second or third pronouncement of divorce does not take effect, and the children are legitimately his. If your husband reconciles with you before the expiry of the waiting period, then the second pronouncement of divorce is effective. The validity of reconciliation does not require the wife's knowledge or consent, and reconciliation may occur through intercourse or its preliminaries according to some scholars. The third pronouncement of divorce is effective if you are still married to the husband, and with it, you become unlawful to him until you marry another man in a valid marriage. Pregnancy does not prevent the occurrence of divorce.