To the question of whether or not Americans should be called Yankees, I'd say it would make more sense to call someone from Ireland "British" than to call people from most of the US "Yankees".

In the United States, Yankee has two meanings. The most accurate is that Yankee refers to people from New England. The less accurate is for people from the South as it existed during the Civil War to call anyone who was from the North as it existed during the Civil War a Yankee. Since about half of the US wasn't part of the US during the Civil War, that leaves out most of us.

It's always interesting looking at what people call themselves compared to what people from elsewhere call them. I once played music with a guy who had Celtic stars in his eyes. He thought all music from what we (probably inaccurately) refer to as the British Isles was Celtic music. We finally had to tell him he couldn't introduce the English music we were playing because he'd almost always refer to it as Celtic.