Is it permissible to propose to a girl after having engaged with her in forbidden acts, and what is the expiation for this sin? Does what happened constitute zina (fornication/adultery)? And does this fall under the meaning of Allah’s saying: "Wicked women are for wicked men, and wicked men are for wicked women"? And will this affect their marital life?

The interaction between young men and women is a path to temptation, and what transpired between you is a testament to that. You must repent and sever your relationship with the girl. If you inquire about her through trustworthy individuals and her righteousness becomes apparent to you, and she repents, then there is no legal impediment to proposing to her and marrying her, for "nothing like marriage is seen for two who love each other." You must perform Istikhara (prayer for guidance), and whoever repents, Allah accepts his repentance. The noble verse: "Wicked women are for wicked men, and wicked men are for wicked women" does not apply to you, as its meaning refers to chastity being a condition for the validity of marriage.