Is it permissible for a girl to marry herself to the young man with whom she committed fornication and then repented, based on the Hanafi school of thought and the hadith that states that an adulteress marries herself, in the event that her family refuses to marry her to him?

If you both have repented sincerely and truly from the indecency, then your marriage is permissible, and the description of "fornicatress" is removed by repentance. It is not permissible for a woman to marry herself, as marriage without a guardian is not valid according to the majority of scholars. The aforementioned hadith does not indicate the permissibility of a fornicatress marrying herself; rather, it is a prohibition against it. If the guardian prevents the marriage without a valid reason, he is considered an adil (one who unjustly withholds a woman from marriage), and it is permissible to refer the matter to a judge or for the more distant guardian to marry you.