A video showing all costumes:
https://www.youtube.com/watch?v=YiPxG9fGHHc
You can change costumes anytime you want during a game by using a suitcase in your inventory. Given the amount of costumes Rebecca has it's a great idea.
And our concerns turned out to be true, Billy was robbed.He has only 4 costumes: his default one, the mafia suit, Cody's costume and wolf force costume.
Are all costumes unlocked from the beginning?