What should a girl do if a young man committed adultery with her, then left her intending to marry another, and should she perform Istikhara or leave the matter to Allah, and should she remain in contact with his family?

The relationships that arise between a young man and a young woman, starting with admiration and ending in committing indecency, are forbidden and sinful. This is because they are مقدمات (precursors) to zina (fornication/adultery), which is prohibited by Islamic law. This relationship is built on falsehood, and both parties must repent from it and sever it. Repentance necessitates regret, cessation, and a firm resolve not to return to the sin. Salat al-Istikhara (prayer for guidance) is not legislated in this situation, because Istikhara is for permissible matters. As for prohibited and obligatory matters, there is no Istikhara for them. The obligation here is sincere repentance and severing the relationship. It is not permissible for the girl to wait for the young man after he has refused to marry her. If the young man repents and then wishes to marry her, there is no harm, but the girl is not obligated to wait for him.