Since I like dragging shit like this up, and I was at work when the question was asked:
The Flyer is something of a joke, in that, while it's for a real seminar and was about being inclusive to all the weirdos, it used the ridiculously long acronym specifically to highlight the number of different identities covered by the "LGBTQ" label.
As to your specific questions:
Two-spirit refers to the fact that Native American tribes had pretty diverse and distinct cultures from one another, some of which allowed for some very precise distinctions, that may not precisely translate to English/Modern American gender sensibilities, but in many tribes, there was an understanding that a person could somehow get two souls, and thus could, in some ways, be treated as a member of the other gender (or even of a completely separate gender with its own rules. An easy example of this is in marriage: many tribes didn't allow same-sex marriages, but some that didn't DID allow for their two-spirit to marry either side, or both over the course of their life. ) Rather than create a different classification for EACH tribe's specific stance (the Cree, for instance, have 6 different gender-defining words on their own, beyond just "man" and "woman"), they're summarized as "twospirit".
Resexual may have been the flyer makers getting tricked, because I can't find any real evidence of the term BEFORE the flyer existed. As of now, the consensus is that, if it IS a thing, it refers to people who are just unable to move past their exes.
Allies, are, well, "allies". People who don't identify as anything weird, but think it's fine for the weird guys to be weird, so they show up to events and support them.