I agree that zinc is one of the important micro-nutrients but people require a balanced blend of food for our biological engines.

Africans are not as tall as northern Europeans. But Manute Vol and other sports figures in basketball and football receive a lot of press coverage.

There are some effects of the biome. Compact bodies tend to conserve heat relative to linear ones. This can affect average height as well as body proportions. The study participants Europeans and Americans do not fall into the range where this effect is powerful, however.

Taller people tend to earn more on average, although the effect is modest. This is clearly true in occupations where strength is important but also a relationship exists in other occupations as well. It could be perceptions, as you say or something systematic. It's somewhat of a mystery.

The English were relatively short in the mid-nineteenth century and so their expeditions return with stories some exaggerated, not doubt about giants who lived in other parts of the world.

People tend to shrink with age, especially after age 50 or so. It has to do with spaces between the joints amount of cartilage and posture. Bone length does not change.

The second and third generation effect of immigration accounts for only a small portion of the height shortfall between Americans and northern Europeans. Besides the slowdown in American heights began in the 1950s, well before large-scale immigration into the country.