After you put on the entertainment uniform for the host club you are still allowed to walk away and play the gauntlet. Not sure if this is intentional but it doesn't seem so since the art for the battles is the normal jacket uniform.
Yup, that's intentional. Once he's decided to he's decided to, but I didn't have the time budget to do a whole unique set of battle standees for that outfit. So unfortunately that can't be represented 1 to 1.