You definitely have to define bitcoin as money. It has all the required features, and it is used in exchanges.
That's not a good reason to classify bitcoin as money. Bitcoin has additional features that money lacks. We don't have a word for it yet but what ever Bitcoin is, money is a subset of that.
Exactly. Bitcoin is more than any other money ever was. What other money can move from here to the other side of the world faster than I can make dinner?