1. What is the estimate of h^2?

Narrow sense heritability is the proportion of the phenotypic variation that is due to the additive effect of the variation in the genes of the human. It is found by dividing the additive genetic variation of a trait by the phenotypic variation of a trait-

VA / VP = VA / (VA+VD+VE).
The narrow sense heritability estimate for Huntington's Disease is 50%, as a child with a HD parent has a 50% chance of inheriting the allele. There is no environmental variation to be factored in, as HD is a genetic autosomal dominant disease.

2. How much influence does selection have on this trait?

Research suggests that selection is weak on Huntington’s in human populations. The weak selection coupled with mutation keeps it from becoming extinct. Huntington's is a genetic disease that easily evades natural selection because it is often “invisible” to natural selection. This occurs because it does not normally affect people until after reproduction. The reason for its escape from selection is because the disease has a late-onset period. As a result, Huntington’s survives into future generations despite its deleterious effects. Huntington's is rare but it is not entirely eliminated because selection does a relatively poor job of weeding these alleles out, while mutation continues creating new ones.

(http://evolution.berkeley.edu/evolibrary/article/_0_0/medicine_05)

3. What effect would inbreeding have on this trait?

Inbreeding would increase the chance of Huntington’s because it would make the dominant allele more frequent. Looking at the figure below one may infer that when the dominant allele is present then the chances of the offspring carrying Huntington’s double. If inbreeding were to occur, it could make it possible for an offspring in the next generation to have two Huntington alleles. This would only occur if the two with Huntington’s were to inbreed with one another. As inbreeding continues to occur it will increase the likelihood of the disease to be present in the population over time.

(http://evolution.berkeley.edu/evolibrary/article/_0_0/medicine_05)