Short answers, pulled from the story.
In biology, a hybrid is the offspring produced by combining the qualities of two organisms from different varieties, subspecies, species, or genera through sexual reproduction. Each cell of a true hybrid contains genetic material from two different organisms, distinguishing it from a chimera, in which only some cells carry a different organism's genes.
Sterility in hybrids usually results from a mismatch in chromosome numbers between the two parent species, which prevents orderly cell division during meiosis. The mule, for example, has 63 chromosomes because a female horse (64 chromosomes) and a male donkey (62 chromosomes) produce offspring with an odd number, making viable sperm and eggs impossible to form under normal conditions.
Between 1% and 4% of the DNA of people living today outside most Sub-Saharan Africa is of Neanderthal heritage, according to the Neanderthal genome project's 2010 findings. Analysis of 600 Europeans and East Asians showed their combined genomes covered 20% of the Neanderthal genome now present in the modern human population.
Hybrid vigour, also called heterosis or heterozygote advantage, is the phenomenon where hybrid offspring are stronger, larger, or otherwise more robust than either parent. Ligers, the offspring of a male lion and female tigress, grow much larger than either parent species, while hybrid maize provides a considerable seed yield advantage over open-pollinated varieties.
Many of the world's most important crop plants are hybrids. Bread wheat, Triticum aestivum, is a hexaploid hybrid of three wild grasses. Triticale is an intergeneric wheat-rye hybrid. Commercial fruits including loganberry and grapefruit are hybrids, as are the herbs peppermint and the London plane tree.
The kunga equid hybrid is the oldest known animal hybrid bred by humans, produced as a draft animal and status symbol roughly 4,500 years ago at Umm el-Marra in present-day Syria.