Is it permissible for a young Muslim man to marry a foreign girl who converted to Islam after they had committed fornication, knowing that they both regret what they did? And does her re-uttering the Shahadatayn (the two testimonies of faith) before the Imam prior to the marriage contract count as repentance for her? What should they do now, considering they have a daughter?

Adultery is a grave sin, but sincere repentance erases the sin. Repentance is achieved through remorse and does not require the Shahadatayn (the two testimonies of faith). Some scholars stipulate repentance and a waiting period ('istibra') for the validity of marriage to an adulteress, and the child is attributed to the husband in all cases. One must beware of the devil's machinations, and the guardian (wali) is a condition for the validity of marriage. A Muslim's residence in non-Muslim lands is not permissible except out of necessity or for a legitimate Islamic interest.