Is it considered an oath requiring expiation for someone who intended inwardly to refrain from a certain action, then uttered the word "I swear" without completing the statement and without intending to utter it, and then did what they had sworn to avoid? And does expiation apply to someone who intended inwardly—whether intentionally or unintentionally—that they would be an unbeliever if they did or did not do a certain thing, and then violated that intention, and does expiation become obligatory upon them?

An oath is not binding unless it is uttered. What is in one's mind has no consequences. If an oath is uttered unintentionally, it is considered a 'laghw al-yamin' (a frivolous oath) for which there is no expiation. If someone does not complete their oath or does not mention the object of the oath, their oath is not binding. If one swears by kufr (disbelief) or by a religion other than Islam, the person should seek forgiveness and repent to Allah, and there is no expiation for them. Swearing by other than Allah Almighty is a major sin.