Regarding fact 2. Tolkiens idea for a magical ring came primarily from the scandinavic Volsungen saga which he studied intensly. While he also drew inspiration from Nibelungenlied, he certainly did not get his idea for a magical ring from the Wagner adaptation called Ring of the Nibelung. Tolkien himself even denied influence by Wagners ring of the Nibelung. Which by the way would be considered germanic and not scandinavic. So fact 2 should say: The concept for a magical cursed ring came from Norse mythology, specifically the story of the Volsungen saga.