Is the wife truly divorced from her first husband, given that he did not utter the words of divorce, and that the divorce and subsequent marriage procedures to another person were carried out in an illegitimate manner?

If the husband utters an explicit divorce, it is effective even if he was joking or you did not hear it. However, if the authorized official wrote it symbolically without the husband uttering it, the divorce does not take effect, and you remain his wife. Your second marriage is null and void in any case, because it occurred while you were still married to your first husband or within your waiting period (iddah). Therefore, it is necessary to ascertain whether the husband explicitly uttered the divorce or not. If he did utter it, did he reconcile with you verbally during the waiting period? If so, you are his wife; otherwise, you are not permissible for him except with a new marriage contract. You must repent for deceiving your husband.