If you define "true" American cuisine as something that is (a) only eaten in America and (b) eaten consistently throughout America, you've come up with a definition that probably nothing fits. Though: watch the British Bakeoff episode where they attempt brownies, one possible contender.
Lots of stuff is probably only gettable in America! I doubt you can get a good cheese steak, italian beef, po' boy, biscuits & gravy, or scrapple in Europe. But you can't get a good version of all of those in most places in America, too.
> [a sentence about caesar salad that disappeared]
Sure. But not at a generic restaurant; you'll have to go to a specifically Chinese restaurant. I guess you could argue that you'd have to go to a western restaurant for Caesar salad, but at least where I am now you'd be more likely to find a Caesar salad in a "european" restaurant than in an "american" one.
America is huge. There is American food, universal throughout the 50 states, but almost definitionally anything that's 3,000 miles successful is going to be popular outside of the US as well.
There is no such thing.
Well, sure, but so what? At the point where something's popular worldwide, to the point that people draw on it without thinking of it as from somewhere else, it's not a cultural thing anymore.
> Ooh, here's a fun one! Craft beer. It's pretty interesting watching American beer styles migrate over to Europe.
Craft beer very much came out of the UK with CAMRA and British traditional ales, American involvement came later. What we have now is very much international with influences in all directions, not an American culture spreading out one way.