Kingdom of Knuffel

You have a cat, with wings

Your familiar's a majestic white stag.

You have a sleek-looking Barn owl.

You have a parrot for yours.

I would think you have a bee

I think you have a white Betta fish

You have a parrot, the kind that talks.

You've got a ribbon seal!

Because pinnipeds are cute.
Also occasionally terrifying.
Both also seem to describe your current avatar, so there you go. Perfect fit!

Your familiar is a tiny tiger... Or maybe it's just an orange cat ?

You've got a devious imp as your familiar.