Are the sins of a Muslim who disobeyed Allah by committing major sins and repented with sincere repentance forgiven? And should he marry the girl with whom he had a relationship if she embraces Islam, or should he seek another Muslim woman to start a new life?

The feeling of guilt and remorse over it is a sign of divine grace from Allah. One must abandon sins, express sincere regret, and resolve not to return to them, without despairing of Allah's mercy. You must cut off your relationship with the woman for fear of relapsing into sin, and distance yourself from the environment that led to it. You may seek help from trustworthy women to invite her to Islam. It is not permissible to marry her in the state you described, as she is not chaste. It is advisable to marry a religious Muslim woman who will assist you in obedience and preserve your faith.