Is kissing considered direct adultery? And does the wife remain lawful to her husband? And is expiation required of her after her repentance and remorse?

What happened is not adultery that necessitates the prescribed punishment (Hadd) nor does it affect the marital bond. It does not require expiation other than sincere repentance, which includes abandoning the sin, feeling remorse, and resolving not to return to it, along with concealing oneself and not publicizing the act. Among the signs of sincere repentance are avoiding the causes of the disobedience, cutting off communication with non-mahram (definition) individuals, and striving in obedience to Allah.