The real problem with Asuka is that she's more or less a very believable 13-year-old girl that never grew up. And not in the cultural or behavioral "oh, she never matured" sense, no, she literally can't get any older than 14-years-old.
In the series she doesn't get the chance; but there's no reason to suppose that she won't continue to grow and develop after EoE
, as Bagheera suggests in his fic: Ghosts of Evangelion
. The complicating factor in understanding her in the series is her precociousness, which comes from her early need to prove herself (though the capability
is presumably in-built).
, the third Rebuild
film, the notion of "the Curse of Eva" in introduced, keeping her body as a teen while (presumably) her mind continues to mature (on top of similar precociousness). We have not (yet) been shown any other in-universe consequence of this to justify it, so at present the evidence is that this is purely a marketing gimmick*; though why an older Asuka in addition
to the younger wouldn't be marketable I have no idea - no one seems to mind that Misato is older.
* Most obviously it enabled them to make trailers without revealing the major feature: the time skip.
As for misunderstandings - I guess that people probably misunderstand Asuka (and Shinji, and...) about the same amount as they misunderstand people they don't know intimately in real life.