How would selection against heterozygous individuals over many generations affect the frequencies of homozygous individuals? would the results of such selection depend on the initial frequencies of p and q? could you test this experimentally?

The selection against the heterozygous individuals would influence the frequencies of the homozygous individuals for many generations. If the selection of heterozygous individuals is not done, the frequency of the heterozygous individuals may decline in against the homozygous individuals.  

Yes, the outcomes rely upon the initial frequencies of p and q of Hardy-Weinberg allele frequencies. An inference can be formulated in order to test the experimentation. For example, use Hardy-Weinberg equation for allele frequencies in a population, that is,  

p2 + 2pq + q2 = 1, where p and q are the homozygous individuals, and 2pq is heterozygous. In the mentioned equation, the heterozygous individuals, that is, 2pq decreases and homozygous individuals, that is, p2 and q2 increases.  

meteorologists would compare a new weather map with one 24 h old to see how fast a front is moving.

"do a testcross with a homozygous recessive plant."