The most important thing to use is the brain. Why the outlier? Is it more likely to be a genuine result or a data error. Sometimes other variables may suggest a true value.
If you cannot tell then carry out the analysis with a smaller weight associated to the outlier. Carry out a sensitivity analysis to see how much difference including the value as normal (w = 1) and excluding it (w = 0) makes. Report on these differences in the conclusion.
whenever it can be
No, median is not an outlier.
0s are not the outlier values
The assumption in the question is not valid. There are two main reasons for outliers: one is that there is a measurement or recording error and if that is the case, then the outlier should be excluded. However, it is possible that the model under consideration is no longer valid when you get near the outlier.
Depends on whether the outlier was too small or too large. If the outlier was too small, the mean without the outlier would be larger. Conversely, if the outlier was too large, the mean without the outlier would be smaller.
The answer is outlier
No. A single observation can never be an outlier.
Outlier does not affect the median.
The answer depends on the nature of the outlier. Removing a very small outlier will increase the mean while removing a large outlier will reduce the mean.
Calculate the mean, median, and range with the outlier, and then again without the outlier. Then find the difference. Mode will be unaffected by an outlier.
The outlier is 558286.
1,2,3,4,20 20 is the outlier range