Plant cell already has nuclear DNA.

If race were proved to be not based in biology, that it was merely a social construct, wouldn't this statement require an extensive study of gene frequencies in nuclear DNA? For example, let us say that blacks in America truly have a genetic advantage in sports such as basketball and football, to refute or substantiate this claim there would need to be a study of large populations measuring athletic ability (as a series of genes) and mapping the frequencies across already established racial lines. Is this true?

Mitochondrial DNA codes for about 13 proteins (depending on the species of organism). These 13 proteins account for a small proportion of the proteins present in mitochondria. The remaining proteins are coded for by nuclear DNA. What is the most likely explanation for how these proteins find their way to the mitochondria?

What is the difference between the inheritance of mitochondrial and nuclear DNA, and what advantages and limitations doe comparisons of mitochondrial DNA offer for establishing genetic relatedness?