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Yes, a standard deviation of 4.34 can be correct. Standard deviation is a measure of dispersion or variability in a data set. It represents the average amount by which individual data points deviate from the mean. Therefore, a standard deviation of 4.34 simply indicates that there is some variability in the data, with data points on average deviating by 4.34 units from the mean.
Units of measure do follow the standard deviation.
Standard deviation is a measure of the spread of data.
BMI varies from person to person and one measure of this variability is the standard deviation. Assuming the BMI is approximately normally distributed, only around 0.135% of the people will have results that are -3 sd or lower.
The standard deviation is a measure of how spread out the numbers are. Three points is needed to calculate a statistically valid meaningful standard deviation.