If I'm not mistaken, a question of the form "If I asked you Q, would you say A?" is the same as asking "Q xor (A means yes) xor (you are speaking the truth)". That is a direct question, which is part of the enumeration.
> And you haven't answered about 4. Or 9.
Umm...yes? I didn't intend to. But if you insist, 4 is not a logic puzzle, and 9 is easily solved in principle but possibly prohibitively long to calculate in practice. Compared to humans, computers are relatively less bad at finding a guaranteed winning move than at playing Go well, so you can't necessarily conclude that because humans play Go better than computers, they would also be able to solve that puzzle faster than computers.
In particular, I think you'll find the solution to 2 does not fit in your scheme. At least, not as far as I understand it. I'd like to see your scheme for enumerating possible questions fleshed out in more detail, but I don't think I believe you.
And you haven't answered about 4. Or 9.