He may not be good, but he is good at research.
I think being non-vegetarian is less evil than being a morally inconsistent non-vegetarian. If you would have moral trouble being introduced to your food (or raising it) then you shouldn't be eating it.
The status quo is preferable when other option is of unknown goodness and irrevocable.
As the sword killed 90% of those who touched it, Vhazhar could have, upon reading the records, discovered that the sword only allowed to survive those who help increase the CEV for sentient life (and thus slaughtering a ridiculous number of Cohen-esque "heroes").
It seems that most the discussion here is caught up on Omega being able to "predict" your decision would require reverse-time causality which some models of reality cannot allow to exist.
Assuming that Omega is a "sufficiently advanced" powerful being, then the boxes could act in exactly the way that the "reverse time" model stipulates without requiring any such bending of causality through technology that can destroy the contents of a box faster than human perception time or use the classical many-worlds interpretation method of ending the universe where things don't work out the way you want (the universe doesn't even need to end, something like a quantum vacuum collapse would have the same effect of stopping any information leakage in non-conforming universes).
This makes the not-quite-a-rationalist argument of "the boxes are already what they are so my decision doesn't matter, I'll take both" no longer hold true.
True, however assuming the cannon limitation on apparition distance and broomstick speeds, he could search the UK pretty quickly, followed by Europe.
In this instance Quirrel probably realized something of the problem with good and powerful wizards could not cast Patroni and thought that Harry's absolutely odd way of thinking of things might be able to solve it. It would make sense that he should do this quickly as his plans to turn Harry into a Dark Lord might get in the way of this.
Well, what would Schiner be like with the Eye of Vance? When you can easily protect yourself from non-movie-plot problems through magic coupled with amazing situational awareness, the movie-plot problems get to be what's left (not to mention that the wizarding world seems to breed movie-plot villians).
On the topic of Mad-Eye, as it has been established that Mad-Eye can see everywhere, why doesn't he go pick up Bella while she is weak?
Given that the magical community didn't seem to get into mathematics much, and provably strong crypto needs a ton of math, I could see how they never went beyond Caesar Ciphers.