y might one trait be more popular than others in a particular population?
A trait may be more common in a certain type of group because of the way this group has changed to adapt. Example: Latin Americans are less sensible to the sun due to that their past family has needed to adapt to the sun.
Is it possible for an offspring to have a phenotype that neither the father nor the mother has?
It is possibel if someone before their parents has that same trait. Example: I can have green eyes like my grandfather, while neither of my parents have green eyes.