It's not like she can make a new one or buy one with her remaining money. No, that would be silly!

1) Yes, that's clearly Ponyville in the flashback
2) Trixie would have no reason to go to Ponyville in between Boast Busters and Magic Duel except to retrieve the cart
3) The graffiti would have to happen when she left the cart unattended. Seeing as she lives in the cart, this would rarely happen… except, of course, we know the cart was unattended when she fled Ponyville after Boast Busters