What is the ruling on this intense jealousy over a female friend getting married, and what is its cause, given that there were previous illicit practices between them from which they have repented?

If you both repent sincerely for what occurred due to ignorance and heedlessness, then, Allah willing, that will not harm you. For, "The one who repents from a sin is like one who has no sin." As for the strong attachment between you, it is not permissible to continue it. Legitimate love should be for the sake of Allah, not an infatuation. You must refine this feeling, and your love for her should be love for the sake of Allah Almighty. You should expand your social circle, and ask Allah Almighty to purify your heart from every blameworthy attachment, and have a good opinion of Allah that your relationship may continue even after your marriage. Your asking Allah Almighty that you both not marry is impermissible and may be considered an transgression in supplication. If you truly love her, then you would wish good and righteousness for her, and this is true love. So, strive to rationalize this feeling and control it according to the Sharia (definition).