I'm afraid that changing the class of a character is not possible in the way that it is to change the race, gender, appearance, or name. My understanding is that this primarily due to the way the skill tree for each class does not match up with those from other classes. To be perfectly honest, I do not anticipate class changing a character to ever be available in TERA.

Once equipped and bound, costumes are intended to be used only by that one character. This is the reason we do not move bound costumes (or mounts) between characters.