Short answers, pulled from the story.
Beech is the genus Fagus, a group of deciduous trees in the family Fagaceae. The family also includes oaks and chestnuts, and Fagus is the first diverging lineage within it. Beeches are native to subtropical and temperate parts of Eurasia and North America.
There are 14 accepted species of beech in two distinct subgenera, Englerianae and Fagus. Subgenus Englerianae is found only in East Asia, while subgenus Fagus is native to Europe, western and eastern Asia, and eastern North America.
European beech, Fagus sylvatica, yields a tough timber weighing about 720 kilograms per cubic metre that is used for furniture, flooring, plywood, household items, chalets, houses, and log cabins. It also makes excellent firewood, smokes Westphalian ham and andouille sausage, and is used in fermentation tanks for beers such as Budweiser.
The common name beech comes from the Anglo-Saxon boc, bece, or beoce, related to the German buche and Swedish box, all of which also meant book. The connection arose because old Runic tablets were made of beech wood, and beech wood tablets served as a writing material in Germanic societies before paper.
Beech trees are affected by the beech blight aphid, beech bark disease, and beech leaf disease. Beech bark disease involves scale insects and the fungi Neonectria faginata and Neonectria ditissima, while beech leaf disease is spread by the nematode Litylenchus crenatae mccannii and was discovered in Ohio in 2012.
The oldest fossils assigned to the beech lineage are pollen grains 81 to 82 million years old from the Late Cretaceous of Wyoming. The two subgenera, Engleriana and Fagus, diverged from each other in the Early Oligocene, between 32.1 and 33.4 million years ago.