HalFinney comments on Wrong Questions - Less Wrong
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I can take a shot at a couple of these. For free will, suppose it turns out that neural activity is not fully determined by mechanistic principles, but is in some cases determined by thermal/quantum noise. And yet, it turns out that out of that noise, certain neural activity patterns appear seemingly magically. Neurons A, B and C fire together to make a decision, even though the most detailed investigation shows that whether they would fire or not was purely random. And yet these correlations appear persistently, too often for random statistical correlations to explain, and correspond to our subjective feelings of free will. A likely model is that there is another, otherwise inaccessible, realm which is influencing neural activity and that the brain is a specially-tuned "receiver" designed to amplify quantum chaos into determinate action. The free will comes from this other realm.
For why anything exists at all, one possibility is the Tegmark/Schmidhuber model where the universe is pure information, part of a much larger information world which has Platonic existence. In this concept, all information patterns and "information objects" have a form of existence, and sufficiently complex information objects look like universes such as the one we observe. These models then aim to impose a measure on information patterns, making some more prominent than others. Suppose these theories can be developed to the point that this measure can be computed, and it turns out to predict that there is by far one highest-measure information pattern which includes conscious entities. And further, that that information pattern corresponds in 100% agreement to our universe, even to the point where it computes that we ourselves, we human beings, are by far the most prominent conscious information patterns in the informational multiverse. Then I think this would be a very strong candidate for an explanation of why anything exists, and in particular why the observed universe and we observers exist.