Well, what I'm going to do is start by sorting out your thinking. No electron is weird. All electrons are identical - give or take their spin - so it isn't the electrons that are weird, but the behaviour they are exhibiting in single-layer graphite.
Fairly obviously, they act like a two-dimensional gas in this environment and you have to understand their behaviour in that context. I don't know any quantum mechanics worth a damn - Kevin Alyward might be better off - but I do know enough to know that a two-dimensional electron gas is going to behave in thoroughly weird ways.
---------- Bill Sloman, Nijmegen