Yes, I agree that these are important questions. I think I would break your question up into two:
Q: How can we find good questions to think about?
Q: When should we stop thinking about a question?
Now, I must confess, I'm a fan of the root question that I've already come up with. But after I think about it some, I begin to think it may make sense to ask multiple root questions, all of them fully general, and all referring to each other. The problem of rationality can be looked at in different ways, and I imagine these ways can complement each other.
NTS: the "apply a correction, test, repeat" algorithm may make a good root question.
I've been on Less Wrong since its inception, around March 2009. I've read a lot and contributed a lot, and so now I'm more familiar with our jargon, I know of a few more scientific studies, and I might know a couple of useful tricks. Despite all my reading, however, I feel like I'm a far cry from learning rationality. I'm still a wannabe, not an amateur. Less Wrong has tons of information, but I feel like I haven't yet learned the answers to the basic questions of rationality.
I, personally, am a fan of the top-down approach to learning things. Whereas Less Wrong contains tons of useful facts that could, potentially, be put together to answer life's important questions, I really would find it easier if we started with the important questions, and then broke those down into smaller pieces that can be answered more easily.
And so, that's precisely what I'm going to do. Here are, as far as I can tell, the basic questions of rationality—the questions we're actually trying to answer here—along with what answers I've found:
Q: Given a question, how should we go about answering it? A: By gathering evidence effectively, and correctly applying reason and intuition.