"Autosomal dominant"–

Dominant phenotypes are when only one copy of the gene is sufficient to observe the described phenotype. The genotype in dominant genes can be said to be Hh or hH in a heterozygote individual and still see the dominant phenotype. This of course is only applicable to diploid organisms, which is what you are referring to.

Autosomal merely refers to the location of the gene on non-sex chromosomes i.e. X or Y chromosomes.

Meiosis is the method by which haploid cells (sperm–male; ova–female) carry the single copy of the gene, either dominant or recessive. Crossover occurs during the process of meiosis in the prophase I believe. It is merely an increased way of developing diversity in the final sperm or ova cell which will combine during fertilization as to create more opportunities for diversity. Each gene has two copies in our body–we have chromatids connected by a centromere, one from our mother, one from our father. If there was no crossover we would be merely transfering copies of our father’s chromosome or mother’s chromosome sorted via independent assortment.

So, crossover occurs in meiosis and is merely another mechanism our bodies use to increase diversity in gametes, which in effect gives more variation that natural selection can act on and therefore increases the fitness of a population overall over time.

Huntington’s specifically acts like any other autosomal dominant gene. A pedigree (family tree) is the best method of visualizing inheritance.

I’ll give a quick example, but just search google for pedigree analysis, or inheritance.

Let’s say your mother has huntington’s (her genotype is Hh–one copy of the dominant allele and one copy of the recessive allele), which does not show phenotype until late 40s. Your father does not have huntington’s (his genotype is hh). You have a 50% chance of having the disease because, under the rule of independent assortment, which ova that is fertilized by your father’s sperm and becomes you has a 50% chance of having that dominant allele. Punnett squares are another, however simple, way of analyzing this phenomenon.