Yes, that is what it means. :)

That can't be it because the error wouldn't straddle the speed of light. It would put the range at 1.000022c to 1.000080c, both of which exceed c, so they wouldn't have written it off as error.

But that doesn't indicate a hard error bound; this is a statistical matter, after all. Most likely it's just an expected standard deviation.

It indeed is the standard deviation.

A single standard deviation is not enough, normal procedure is to allow up to three standard deviations (or more, sometimes five), which puts the measurement in a range consistent with models.