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Ask in the "Papillon Breedables" SL group for links to Anj's googledocs with more information. (I can't link them here, something about karma.)

Wing mutations?
Tattered+Rainbow = Ribbon.
Hollow+Rainbow = Stained.
Rainbow+Rainbow = specials.
To get 'Eyes', you just have to have a high loyalty bonus
Any rainbow with any rainbow can unlock rainbows E, F, G, H, and Quartz.

All particle mutations are just random dumb luck.

Body mutations?
Ghost body require ghostly wings
angelic body requires sparkling wings
vampire and zombie requires eternal body.
The rest are random.

Do classes mutate, or are they only changed with evolution? They can mutate as well, though it's much rarer. Much more unlikely from a low-tier than it would be from a high tier.