Is it permissible to marry a foreign woman who had a sexual relationship in her past? And is her conversion to Islam sufficient for "Islam to efface what came before it"? And how can one deal with this past in the marital relationship?

Your relationship with this atheist girl is forbidden and sinful, leading to temptation and illicit love. You must repent from it and sever all ties with her. It is not permissible for you to marry her because she is an atheist, and marrying a polytheist is unanimously forbidden, except for women of the People of the Book under specific conditions. Your continued association with her for the purpose of inviting her to Islam is not permissible because it is a cause for temptation. However, you can direct her to good people to invite her. If she embraces Islam, repents, and abandons forbidden relationships, then there is no objection to you marrying her. Do not investigate her intentions, as that is among the secrets (of the heart), and her outwardly embracing Islam is sufficient.