The EU-related structures in Brussels are about as united/fragmented as the US Congress, indeed.
But the national governments are nothing like US state governments. A lot more political fragmentation, plus they still consider themselves executives of sovereign nations with various vital interests and also historic resentments. Few Californian politicians will base their programs on suspicions towards New Mexico. In Poland, "don't kowtow to the Germans" is still a living idea and current PM Tusk is regularly accused of doing precisely that.
Exactly. I'd even go as far as saying German overreach and arrogance ten years ago killed the EU for good. Before that it genuinely felt people were at least trying. Now it's a walking corpse.
The European nations are not unified similarly to the USA because we do not have the common history of being a bunch of immigrant colonies glued together.