Results are out now, did you get your tickets?
Since it's an arena i guess the chances of getting a ticket are high but at the same time this "tour" is only limited to two days so maybe the chances aren't so good, but I don't see why they wouldn't allow TA fans to get tickets for arenas because if I were the team I would want the shows to be sold out.
As for the letter, I honestly think that the staff will not allow anything to be given to ayu, at best they will take your letter to seem polite but they will just put it in the trash afterwards. I might be wrong though but i don't think you can give her anything at the venue. If you want to write her something there is this section on the TA website where you can write ayu a message and hope that she reads it.