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The mean would be negative, but standard deviation is always positive.
No. It is defined to be the positive square root of ((the sum squared deviation divided by (the number of observations less one))
It means that the observed value is greater than that which might be expected under the model being used. Often, it is deviation from the [arithmetic] mean.
The SD is the (positive) square root of the variance.
No. The square of a number is always positive, so the sum of several of them must also be positive.