Is it permissible to supplicate for marriage to a specific person, knowing that he is engaged to someone else and loves me? And is it permissible to supplicate that he divorce his fiancée so that he may marry me?

Supplication is an act of worship. It is permissible for a Muslim to ask their Lord for all that concerns them, regarding their religious and worldly affairs, whether in prayer or otherwise. However, transgressing in supplication is not allowed. Part of transgression is asking Allah for what is impermissible, such as harming a Muslim. Therefore, your supplication for a suitor to leave his fiancée so that he marries you is an act of aggression and injustice against her. It is not permissible for a woman to ask for the divorce of her sister (in faith) so that she may marry (her husband). You must be content with what Allah has decreed for you and ask Allah to facilitate a righteous husband for you.