Does divorce occur in the mentioned cases, and is what Ibn Taymiyyah said about innovative divorce considered correct?

First: The saying, "What was between us has ended, go to your family," is an allusive divorce (طلاق كناية) that takes effect with intention. If the intention is unknown or forgotten, the default is that no divorce has occurred.

Second: The ruling on divorce for the second and third times depends on the of juristic opinion (fatwa) of the muftis.

Third: Caution must be exercised against being lenient with the words of divorce due to the consequences that ensue. It appears from the question that the questioner is reckless in this matter, which necessitates that divorce should befall him, just as Umar (may Allah be pleased with him) did when people became lenient with the triple divorce.