Hm. I am not a 100% computationalist, but let me try.

1. b) 80% c) 15% a) 5% (there should be a physical structure, but its details probably don't matter. I can imagine several intuition pumps supporting all answers).
2. Don't know.
3. There is an isomorphism between instantaneous physical states of the machine and (a subclass of) mathematical formulae, and the machine went from a state representing "2+2" to a state representing "4".
4. There is an isomorphism between the physical states of the machine and colors (say represented by RGB) and the machine has arrived to the state whose partner (as given by the isomorphism) is close to (255,0,0).
5. Algorithms. I can learn that a ball is round by seeing it or by touching it and it certainly feels different. However among the algorithms there may be equivalence classes with respect to consciousness.
6. Don't know. I am not even convinced that axiomatic logic would not need to be replaced by something more general before arriving to the said Theory of Everything, or whether such Theory can be constructed.
7. (If such a Theory exists, then) no 75%, yes 25%. Partly depends on what "explain consciousness" means: if by "explanation" we mean a set of statements which, when properly communicated, cause people to feel that there is nothing mysterious with consciousness, there may be some need for qualia. Strongly depends on meaning of "qualia": the definition presently used by philosophers will probably be useless for any axiomatisation.
8. Consciousness isn't a binary property, so, in some sense, yes (90%).

By the way, upvoted for asking interesting questions.