I understand some "immune" rulings, but I don't know about an immune enemy's shadow cards. So a couple of questions...

For an immune enemy, can you cancel and/or discard it's shadow cards?

For instance, can Burning Brand still cancel them? Also, can Armored Destrier and Shadows Gives Way discard them?

I think they should all work. Think of it like being able to cancel damage on Beorn. Further justification: The Balrog specifically makes its shadow cards immune to player card effects as well as itself. There'd be no reason to do this if these cancellation effects didn't work on shadow cards of immune enemies.