Yes, although the z-scores associated with p-values of 0.01 and 0.05 have special significance, perhaps mostly for historical reasons, all possible z-scores from negative infinity to positive infinity have meaning in statistical theory and practice.
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s is the standard deviation of a sample. It is difficult to know what you are asking. I will note that there is a statistical programming language called S-Plus, see "Modern Applied Statistics with S-Plus, by Venables and Ripley. I also note that "s" is also used commonly in statistics as standard deviation of a sample. That's about all that comes to mind.
All statistics are data because all statistics are formed of numbers and numbers are a type of data (numrical). But not all data is statistics because not all data is numbers, it can also be words, pictures etc. It's like saying all apples are fruit but all fruit are not apples.
Inter-quartile range, other percentile ranges, mean absolute variation, variance, standard error, standard deviation are all possible measures.
Nearly all the values in a sample from a normal population will lie within three standard deviations of the mean. Please see the link.
'Mean', 'mode', 'median' and 'standard deviation' are all quantities used in statistics. Each one is an attempt to use a single number to describe the essential nature and character of a bunch of numbers.