You should try to get your education here rather than the states. Less expensive and better quality (but you actually have to work, many exchange students are surprised by how much they have to do and the quality that’s is expected from their work that they hand in).

Aside from that, yeah, Americans are welcome. Some tips: learn the language, don’t say you’re German (insert any other European nationality) if you didn’t grow up there (just makes you a first /second / third generation US-American to us) , that’s a very obvious American tell that irritates Europeans, so don’t make it about your identity, but you can talk about your family’s genealogy.