Is it permissible for a woman who has committed adultery and had a marriage contract with the adulterer to marry him as a rectification of the error, or should she live without marriage, or marry another person after repentance? And if she marries another, is it permissible to reconstruct the hymen?

You must repent of Zina (fornication/adultery) by abandoning it, regretting it, and resolving never to return to it, while maintaining discretion. Your marriage to this young man is permissible after repentance. If your father solemnized your marriage to him with a valid Islamic contract involving offer, acceptance, and two witnesses, then he has become your husband, and you should not leave him except through divorce or annulment. However, if the contract at the lawyer's office was merely a written document without offer and acceptance, then no marital relationship is established. We advise you to complete the marriage with this young man to achieve discretion. It is not permissible for you to surgically repair the hymen.