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What about minor animations during the expressions?
(Eyes moving around when nervous. Head moving when dizzy.)

Eyes moving is fine, head movement would also be allowed, if there were no new frames added to create the animation, meaning if you're working just with idle skeletal animation, a head bobbing is fine. Turning the whole head to the side etc would be allowed only as a variation on a single body part (i.e. no frames in between). It would also mean you can't have an extra object you can hide/show (hat, mask), you'd have to choose one or the other - one change of body part, or extra object.

Do show/hiding things such as blush/tears count as an "extra object" on the character?

No, those would be part of facial expressions and free to do without restrictions. The extra object would be something like a hat, or a magic orb, etc. that very clearly changes the visuals.