sounds like the US and our illegal mexican problem.
yeah US probably has more foreign people than any country in europe. It just doesn't show that well in statistics because any child born will be US citizen automatically. Not so in europe. If you are Italian couple and live in germany and have a child, the child is still Italian and has no direct right to get a german passport.
It's normally not very easy to get a passport. In many countries you need to have lived there for years to even be able to apply for citizenship. You might need provide references of citizens you know and think you are "a good citizen". Often you need to pass a test that mostly contains questions about the countries history and political system.
But it's very different form country to country. One reasons some europeans are not that found of americans is their ignorance. They just talk about Europe. But europes countries themselves are very different. Like 1000x fold to New York and any place of your choice within US. It' much more than just the languages.
England is much more similar to US than to many (probably most) european countries.
Greek does have problems but compared to the financial issues of USA most european countries are off alot better. There are certain economic rules and statistics you must fullfill to join the EU, Turkey could probably do it if they wanted to but USA would have 0 chance. 0. Too much debt.
All in all Europe sure isn't in worse condition than US. I haven't seen any Arabic labeled signs here yet but i did see spanish ones all over US.
BTW the Europe != EU. I'm actually not fond of the EU. But I also don't need to worry about it because my country was clever enough not to join.