Is his act with the married woman considered one of the major sins, and are repentance, remorse, and desisting sufficient for true repentance, and is he required to seek forgiveness from her husband?

Establishing relationships with foreign women online is forbidden and may lead to major sins. If repentance is sincere and fulfills its conditions of remorse, cessation of the sin, and determination not to return to it, then that is what is required and nothing else is upon the person.