The mean and median are two measures of central tendency. In
introductory statistics many schools include the mode as another
example of central tendency but the mode could well be at the end
of a distribution.
If the distribution is positively skewed distribution, the mean
will always be the highest estimate of central tendency and the
mode will always be the lowest estimate of central tendency. This
is true if we assume the distribution has a single mode.
Yes. Central tendency is the way data clusters around a value.
Even if the distribution of the value is skewed, the median would
be the best indicator of central tendency because of the way the
data is clustered.