Is a person still considered an adulterer and a criminal after repenting, feeling deep remorse, and marrying the woman with whom he committed adultery after her conversion to Islam?

Repentance demolishes what came before it, and the one who repents from sin is like one who has no sin. Allah transforms the evil deeds of those who repent into good deeds. Your marriage is valid if the Islamic authority conducted your marriage contract and she does not have a Muslim guardian to undertake her marriage.