pinatas are nice and simple - you open them for a goodie inside.
fake costumes are a little more complicated than you'd think. They add what is called a "transformation" to your pet. You can then see it on your transformations list on that pet. So say you use a fake party costume on a chibs. That would add the "party chibs" into the transformation list.
The great thing about that is you can then use the quest called Drew to get vouchers (dress for less) and when you've reached the specific number it needs, you can actually change your pet into that transformation.
Transformations also count towards the rainbow fairy, who is pretty giving with the rewards so she's worth doing.
Enchanted feathers are a bit more boring than you'd expect. They have a slight chance they may turn the pet into that costume. So a panda feather might turn a pet panda (if it can wear the costume).
I hope that helps a bit.