I wonder though if there are any authentic American restaurants across the pond, and not just fast food chains.
Not here, at least that I know of. Heck, I don't even know what would be true American food. Care to give some examples?
To people outside the US: What do you normally call my country in conversation? US, USA, United States, United States of America, America, or something else?
Usually we call it US (Estados Unidos, for anyone curious). USA (Estados Unidos da América) is just too long to say, and sounds really formal. América isn't that much used in portuguese while talking about the USA specifically, but we might say "I'm going to America", in which case it is usually assumed we are talking about the States.
To the Brits out there: Every year, Algarve (South of Portugal) is "invaded" by A LOT of english tourists, and I do mean a lot, who come here for the sun and beaches I guess. So much to the point of the portuguese almost looking outnumbered when at the beach (I've been at a small beach with my family in which we were the only portuguese family, no joke). What I meant to ask was, it is something noticeable to us, but is it to you guys there? I mean, are the numbers significant for it to be considered a usual summer destination, or a "thing"?