How can an engaged woman break off her engagement to someone who has not wronged her, especially if she wishes to marry another person who previously met her twin sister?

The general rule is not to break off an engagement except for a valid reason. However, if either party wishes to break off the engagement, there is no harm in it, because engagement is merely a promise of marriage and not a contract.

As for the relationship between a young man and a non-mahram girl, it is forbidden. It is one of the devil's paths and a way to deviation.

The young man must repent from his first relationship and from his relationship with her sister. If he wishes to marry the girl's sister, there is no religious impediment if she and her guardian agree, provided that he approaches homes through their proper doors and proposes to her through her guardian. However, if she or her guardian does not agree, it is not permissible to continue the relationship with her under any pretext.