Suppose we know through logic alone that something is true about the world. I don't know if there are such truths (or even such ways of knowing), but a good candidate might be the claim that no state of affairs simultaneously holds and doesn't hold of the same portion of the world. If considerations of pure logic (assuming there is such a thing) show us that this is really true of the world then they also seem to show that it is true of any possible world--any way that the world might have been. Changing the world's details, and even its physical and metaphysical laws wouldn't seem to affect the status or applicability of logic itself, or of any truths that might follow from it. That seems like a reasonable inference, but I haven't, alas, read Yourgrau's book, and so can't apply it to the existence of time. But maybe someone else can...

That's right. A is a necessary condition for B: B obtains only if A obtains. A is a sufficient condition for B: If A obtains then B obtains. A can be a necessary but not a sufficient conditiion for B. Example: having legs is a necessary but not a sufficient condition for walking (the legs also need to be used in a certain way). And A can be a sufficient but not a neceesary conditon for B. Example: dropping a ball is a sufficient but not a necessary condition for moving it (the ball could also be moved by by throwing it upwards). This is perhaps the most common way of defining these expressions. And I think it reasonably captures our fairly straight-forward and unproblematic usage. But as always, things are more complicated when you scratch beneath the surface. To do so, look at the entry on necessary and sufficient conditions in the Stanford Encyclopedia of Philosophy.

I also find that saying suspicious, though I'm not sure I accept your suggested argument against it (more on that in a moment). I disagree with the saying because there seem lots of clearly impossible states of afffairs: that 2 and 2 could equal 5; that I could both win and not win the tennis match (in a fixed sense of "win"), and, pehaps more controversially, that I could have had different biological parents than I did. (For more on the different senses of "possible" see Alex George's answer to question 71: Is nothing impossible?) In fact, though, I particularly dislike the saying when people use it to generate false optimism. It is not, alas, possible (in the relevant sense) for me to win the olympic marathon, to be an international multi-billionaire, or to be a wildly successful tabloid heart-throb (well, maybe there's still time for that...). And no snake-oil or course of instruction on the internet will change this, even if the packaging proclaims that everything is possible. Now to your argument...