Did the married man wrong the young woman who became attached to him and with whom he overstepped boundaries, by secretly asking her to marry him, and then informing her that the relationship was completely over? And does this necessitate that the young woman forgive him?

Both of you have wronged yourselves with these forbidden transgressions. Your duty is to repent sincerely to Allah -Azza wa Jall-, and this girl has no right over you; rather, the right belongs to Allah. If you repent sincerely, cut off all ties with this girl and others, and replace bad deeds with good ones, then Allah Almighty will forgive you, and you will return as if you had not sinned, as the Prophet -peace and blessings be upon him- said: "The one who repents from a sin is like one who has no sin." And you must stay away from all causes of temptation, such as avoiding free mixing and forbidden glances, for these are what led you to that sin.