Is it permissible for a Muslim man who lives with his Christian mistress and wishes to repent and fast to marry her now, given that tomorrow is the first day of Ramadan, and what is the legal and Sharia-compliant procedure to follow in this case?

Abandoning prayer is an act of disbelief that expels one from the fold of Islam. The Muslim must repent and hasten to do so by abandoning sins and adhering to the rulings of Islamic law, especially prayer, for Allah transforms evil deeds into good ones for those who repent. It is not permissible to marry an unchaste mistress, because one of the conditions for marrying a woman of the People of the Book is that she be chaste. A chaste Muslim man should not marry an adulteress, whether she be Muslim or of the People of the Book. If he wishes to marry her, it must be after his repentance and her repentance from the forbidden relationship. It is better for him to leave her and seek a righteous Muslim woman who will aid him in his religion.