Is what was stated in the first message considered a conditional divorce, a suspended divorce, or any other type of divorce? And what is the ruling on the oath mentioned in the second message?

A Muslim should guard his tongue from hurtful speech, and this is especially important between spouses. One should train oneself to admit mistakes. It is not permissible to swear by other than Allah, for whoever swears by other than Allah has committed an act of disbelief or polytheism. One must swear by Allah or remain silent. What was said to the wife in the first message is not considered a divorce but a threat, and the statement: "I swore that you would not enter it again" is a lie for which repentance is due, and no divorce occurs through it.