Is it permissible to propose to a girl with whom "minor zina" and repeated khalwa occurred, after she repented and regretted and resolved not to return to disobedience, knowing that the girl refuses the proposal out of fear of God's punishment? And how can they be sure that their repentance is accepted? And what is the expiation or the prescribed punishment for their act?

If the minor fornication refers to the preliminaries of adultery, then you must offer sincere repentance and sever the unlawful relationship with the girl. If you wish to propose to her, then approach houses through their doors [do things the right way]. If the marriage takes place, then praise be to Allah; otherwise, move on from her. The expiation for this act is sincere repentance and an increase in righteous deeds, for indeed, good deeds efface evil deeds. There is no prescribed hadd punishment for these matters, but there is discretionary punishment (ta'zir) from the ruler. The girl should know that there is much good in marrying you if both of you repent sincerely.