What role do emotions (as we know them) play in non-physical planes of existence? For example, does anger exist in any form we would recognize as physical beings?

Polaris channeled about Anger already - you can see it in http://www.polarisrising.com/the-nature-of-anger.html. What I find most interesting is the levels of anger there, and how at level 7 anger is really the same thing as Love. They indicated at some other point that all emotions function the same way - that as we all allow emotions to the ultimate manifestation, in utter surrender, we will experience them as Love.

That said, I don't remember anything specifically said about how emotions react on other planes other than that on the Astral plane, being the plane of emotions, emotions seem as physical to beings there as matter does to us here. Brings to mind the special effects of "What Dreams May Come".

No part of our experience ever disappears, however. It expands - often until it's unrecognizable to us from what it started as. There's no bad part of our experience or emotions.