What should a girl do who committed zina with a Christian man and regrets her action, especially since he proposed to her and expressed his readiness to convert to Islam, while she is seeking repentance and fears falling into another mistake by marrying him?

What is required religiously is sincere repentance to Allah for the forgiveness of the great sin. It is not necessary to confess so that the hadd (prescribed punishment) be carried out on you. Rather, conceal yourself and improve your actions, cut off your relationship with this young man, and beware of such sinful relationships that are an entry point for Satan. Be keen on accompanying righteous Muslim women and attending gatherings of knowledge. If this young man embraces Islam and commits to its rituals and his conduct becomes good, then there is no harm in marrying him according to the conditions of Islamic law (permission of the guardian and witnesses). However, if he does not submit to Islamic law after the two shahadas (declarations of faith), then it is not permissible to marry him.