Is the 'urfi marriage that took place between my friend and a girl without a guardian, based on a fatwa that permits it for fear of falling into sin (al-'anat), considered a legitimate marriage, or were they cohabiting unlawfully? And will Allah not look at them on the Day of Judgment if it was not a legitimate marriage?

The majority of scholars hold that the guardian (wali) is a pillar (rukn) of marriage, without whom the marriage is invalid, unlike Imam Abu Hanifa. Citing the hadith: "The ruler is the guardian of her who has no guardian" does not apply here because the woman has a guardian, who is her father. If your friend's following of the fatwa given to him is based on trust in the scholar's knowledge and piety, then there is no blame on him, for an ignorant person is permitted to act upon the fatwa of one he trusts. However, renewing the marriage in the presence of the woman's guardian is the correct action, as it conforms to the view of the majority. The children resulting from this marriage are attributed to the husband due to the uncertainty (shubha) and the belief in the validity of the marriage, for "whoever marries a woman with a corrupted marriage... their child from her is attributed to him, and they inherit from each other by agreement of the Muslims."