Is a wife sinful for offering herself to her husband after the first divorce with the intention of reconciliation, knowing that the husband took her back after intercourse? And is a wife sinful for accepting her husband's reconciliation after the second divorce and the expiration of her waiting period, and without a marriage officiant or a dowry, with the husband claiming the intention of reconciliation?

There is no sin upon you for what you did to your husband to make him reconcile with you the first time. A revocable return (raj'ah) occurs before the expiration of the iddah (waiting period) of a revocable divorce, either by word or action accompanied by intention, or by sexual intercourse even without intention. After the iddah expires, a revocable return is not valid except with a new contract fulfilling the conditions. It is not a condition for its validity that it be performed before a legal marriage officiant (ma'dhun shar'i) or that the dowry (mahr) be mentioned in it. The husband's intention to reconcile with his wife before the expiration of her iddah is not legally recognized unless it is accompanied by a word or an action. Sexual intercourse after the expiration of the iddah and without a valid legal contract is considered zina (unlawful sexual intercourse).