What is the ruling on a Muslim woman marrying a non-Muslim man if the husband embraces Islam? Is it obligatory to renew the marriage contract, and what is the status of the children?

It is not permissible for a Muslim woman to marry a non-Muslim man, by scholarly consensus. The marriage is invalid, based on the Almighty's saying: "And do not marry polytheistic men until they believe." If the woman was unaware of the prohibition, the sin is lifted from her, but the marriage remains invalid. If the husband converts to Islam and they wish to continue, the marriage contract must be renewed according to Islamic regulations. As for the children, they are correctly attributed to their father, because an invalid marriage, if consummated, is considered equivalent to a valid one in establishing lineage.