Well, it could be just the challenge. Mild infatuation. I remember going to this seminar kind of series because of this person, a total (kinda nerdy!) stranger, but after while when I'd see her around, I'd go 'Meh, what was I thinking?' LOL.
Re your signals, lol. Yes, I think you have it worse than I do. I can hold a friendly mode with her if we're acquainted enough already. Hm, if she were interested, yes, you are sending really confusing signals.
Now that you painted a clearer pic about the emailing, that you have emailed back and forth, I think I'm leaning more towards her not being interested in that way, sorry to burst your bubble, because she would've taken that chance to be more personal. Move on, next TA but keep her on your mailing list and hope against all odds she might be interested, nothing to lose.