I agree, tracking down and explicitly stating all the assumptions is very important. It always reveals a lot about the structure of the problem and can help you move forward. However, my goal here was actually to pose more questions than answers and seed a discussion. Usually people avoid hard questions, but I see many clever people around here, so it's a great opportunity to discuss unusual things.
Let me think more about the implicit assumptions in my questions and I will write about them later.
I described some of the implicit assumptions in a new post, as it got too long.I'll try to address the other questions:
All questions are conditioned on the knowledge of the person, who is asking. The optimal answer depends on the person's knowledge and the question. I see the answer as a tool for setting the questioner's mind in a different state. I guess there might be many different answers, which can have the same effect.
Everyone has their own value function, which determines, whether the question is answered sufficiently. And of course, this value function is also conditioned on it's owner's current knowledge, which means that when the knowledge is updated, the value function can change it's output - that's when you realize that you understand nothing and you have to dig deeper.
I'll have to make another post for this.. :)
Well I sketched out one possibility in the OP, but I think I will have to address the question above first for it to make sense.