What is the ruling on messaging an engaged girl and giving her the choice between her fiancé and the questioner, or hinting to her that his affairs are easy and that he wishes to propose to her, given the permissibility of her breaking off the engagement and choosing him? And would marrying her in this situation be considered forbidden?

It is not permissible for you to propose to the girl as long as she has accepted the suitor, because the Messenger of Allah, peace and blessings be upon him, said: "A man should not propose over the proposal of his brother until he marries or gives up." Most scholars are of the opinion that marriage in this case is valid, even though some consider it invalid. Therefore, turn away from this girl and ask Allah to grant you a righteous wife.