Q1: For the Lord of the Chaos Die, I've considered 'The Chaotician', a scholar of chaos theory who had a revelation, and is now as one with Chaos itself. They appear as an academic, forever changed by the wild and unpredictable force they're united with.
Q2: Two possible die faces I've considered are "Entropy" – the driving force of Chaos – as one that might make you reroll dice, and the "Butterfly" – representing the Butterfly Effect, and strange attractors – as one that might make you move several dice around that are furthest away from it in some circumstances.
I love the butterfly idea!!
I really like these ideas. My other suggestion was a cat or feline figure for the lord, but I was just mulling the idea of chaos over and I think a maths focussed idea, including involvement of butterflies, would be wonderful too. You've already come up with a more defined and we'll articulated description and it sounds great to me.