> I have a question, do people really protest in designated areas in the US?
No, people can protest wherever they want as a rule, under the freedom of assembly clause in the first amendment. It's pretty clear, and is well established (as are the exceptions). The wording of Article 12 in the E.U. fundamental rights charter is, by my reading, purposefully more restrictive than how the Supreme Court has generally interpreted "Freedom of Assembly" in the U.S., but I am not an expert on that.
In practice, you sometimes see things like "Free Speech Zones", which are indeed Orwellian, but also controversial and exceptional. You shouldn't think of them as the rule, because you also see things like the CHOP in Seattle.