All of my responses are for what happened last year! I was a participant in the character auction. I was Gendo Ikari (碇・ゲンドウ) and was the second highest bid recipient.
Answers: You can indeed "win" and go on a "date" with someone. Last year this was just an obligation to show up to the dance with them, although I'm sure a smooth talker might be able to get a second date or even a relationship if he or she tried hard enough.
2) You are indeed bidding on people cosplaying characters. I don't understand why you put people in quotes. Perhaps cosplayers aren't really people. An excellent philosophical discussion that we shall save for another thread!
3) There was no crossplay at the character auction last year that I can remember, although I know there was crossplay at the cosplay contest.
4) Auctions go until the bidding stops.
Last year the highest was $80? $100? One of those two.
Hope that helps.
