I am really confused by her behavior ?

so do you think she is interested ?

Why are you sending her messages? Pick up a phone and call her! When you see her, pull her aside and talk to her! You'll get a much better indication of where you stand if you are actually speaking to her.

Also, it could be that she is confused as to which of your personalities she is talking to. Or maybe she thinks you are trying to be as deceptive to her as you are trying to be here.

That ships already sailed Coastal Rat. She's already answered she's busy until mid June.

I' m confused as to why our 2 named poster writes such an involved text, fraught with so many deep emotions, yet calls it "hanging out" as if she's just one of the guys.

You should ask her bluntly!

The only solution for your doubt is to talk her directly. Ask her again for a date, and solve out all your doubts by discussing every doubt and express your feelings in front of her with honestyand romantic way.