Is it permissible to marry a girl who had an illicit relationship with me and with others, and who shows a lack of commitment to religion, despite my desire to adhere to religion?

The correct text of the verse is: {The fornicator does not marry except a fornicatress or a polytheistess, and as for the fornicatress, no one marries her except a fornicator or a polytheist, and that has been forbidden to the believers} [An-Nur: 3]. It is recommended to seek a woman of religion, based on the Prophet's (PBUH) saying: "A woman is married for four reasons: for her wealth, for her lineage, for her beauty, and for her religion. So, succeed with the one who has religion, may your hands be dusty." What happened with the girl regarding the preliminaries of fornication, and her being unveiled, confirms that she will not help you adhere to your religion. If she repents and commits to wearing the hijab, then there is no harm in keeping her. Otherwise, it is better to stay away from her and seek a righteous girl.