Nobody calls Mexicans or Canadians Americans. Nobody calls Brazilians or Peruvians Americans. They maybe North Americans and South Americans but American means someone from the United States. The Canadians and Mexicans I know would be offended if I called them American.
Prominence is a bit more complicated than that. It refers to the height of a mountain or hill’s summit relative to the lowest contour line encircling it but containing no higher summit within it. Everest’s prominence is actually still its height above sea level.