Is it permissible to marry a divorced woman who has a son from her previous husband, who embraced Islam solely to marry her, and with whom she engaged in unlawful acts, knowing that this son was born after these practices?

It is not permissible to assert that the man embraced Islam for the sake of marriage, as this is a matter of the heart. If the man converted to Islam, did not apostatize, and the woman married him with a contract fulfilling all its pillars, then her marriage is valid. As for the forbidden actions during intimacy, she must repent from them. The child is theirs as long as the pregnancy occurred after the marriage, and this does not affect the validity of the marriage or the child's lineage. Even if the marriage were invalid, as long as they believed it to be permissible, the child's lineage is established with his father. There is no impediment to your marriage to this chaste Muslim woman, with the caveat that she remains a stranger to you until you contract the marriage with her. And her discussing her intimate relations with her husband with you is forbidden, and repentance from that is obligatory.