Is he who resolves in his heart never to abandon a particular sin considered to have exited the fold of Islam, or does this apply only to one who deems the sin permissible or defiantly persists in it? And is marriage to a disbeliever considered fornication that expels one from the fold of Islam?

Insisting on a sin does not render a Muslim an unbeliever, unless he deems it permissible (حلّه), and the same applies to the intention to repeat the sin. This is the doctrine of the People of the Sunnah and the Community (Ahl al-Sunnah wal-Jama'ah). The statement attributed to Imam Ibn al-Qayyim is false, as he explicitly stated the opposite in "Madarij al-Salikin," where he said that persistence in disobedience is another act of disobedience, and openly committing a sin while being certain of the Lord's gaze upon it is grave. If one does not believe in His gaze upon it, then it is disbelief (kufr). In "Zad al-Ma'ad," he mentioned that reward and punishment for the deeds of the hearts are true, so sins of the heart deserve punishment, such as arrogance, conceit, hypocrisy, and ill-will.