Is it forbidden to marry a girl who had illicit love affairs in her past, then completely abandoned them before marriage, but has not truly repented to Allah Almighty?

If a girl has not committed adultery that necessitates the prescribed punishment (hadd), then it is not unlawful to marry her. However, it is better for a Muslim to choose a woman of religious commitment and good character. But if she has committed adultery, the preponderant opinion is that it is not permissible to marry her unless she has repented sincerely, fulfilling its conditions: abandoning the sin, regretting it, and resolving not to return to it, so that the characteristic of adultery is removed from her.