Sure, go read the Wikipedia article, that’ll give you a solid foundation! I’d suggest the Conquest of Bread if you’re interested, or google “what is Anarchism”
It’s the other way around - because the establishment has so much to fear from anarchism, they peddle anti-anarchist propaganda. If we renamed anarchism, they’d just do the same thing. Anarchism does exactly what the name implies - against heirarchies.
I’m not really sure I understand what you mean, sorry. Lots of people have misconceptions and some of those misconceptions are intentionally fed to us. You know, propaganda and such? Lots of people have a really skewed perception of what anarchism is, so I guess that makes them wrong about anarchism, if that’s what you mean!