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For the error.log, I assume the errors at the bottom are newer. Is that the correct assumption?

They are ordered by dateline, but how are dateline deciphered? For example, what would this "1368917037" mean?

As for second question - http://www.unixtimestamp.com/index.php Paste it to timestamp and click convert. The one you wrote is "05 / 18 / 13 @ 5:43:57pm EST". Paste few and you'll find out how they're ordered.