It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
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Yes. If much of your data has negative values, it's likely that the mean will be negative, too.
z-score of a value=(that value minus the mean)/(standard deviation). So if a value has a negative z-score, then it is below the mean.
The range, median, mean, variance, standard deviation, absolute deviation, skewness, kurtosis, percentiles, quartiles, inter-quartile range - take your pick. It would have been simpler to ask which value IS in the data set!
positive
It depends on the context. It may mean quiet, unruffled (positive) or it could mean too laid back to do anything (negative).