Yes SD is ofcourse measure of precision
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The more precise a result, the smaller will be the standard deviation of the data the result is based upon.
Standard error is a measure of precision.
No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.
standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.
Standard deviation is a measure of variation from the mean of a data set. 1 standard deviation from the mean (which is usually + and - from mean) contains 68% of the data.