Short answers, pulled from the story.
Butter is a dairy product made from the fat and protein components of churned cream. Churning damages the membranes surrounding fat globules in cream, allowing the fats to merge and separate from the watery buttermilk. The resulting grains are then pressed and kneaded into a solid mass.
Commercial butter is about 80% butterfat and 15% water. Traditionally-made butter may have as little as 65% fat and as much as 30% water. French butter must meet an 82% butterfat minimum, higher than the U.S. standard.
Cultured butter is made from fermented cream and has a fuller, more complex flavor from compounds including diacetyl produced during fermentation. Sweet cream butter is made from fresh cream and can be produced in as little as 6 hours, whereas cultured butter can take up to 72 hours. Cultured butter dominates continental Europe; sweet cream butter is standard in the United States and the United Kingdom.
Ghee is a form of clarified butter that has been heated to around 120 degrees Celsius after the water evaporates, causing the milk solids to brown. This process adds flavor and produces antioxidants that help protect the fat from rancidity. Ghee can be kept for six to eight months under normal conditions.
Butter is traced back to the Neolithic era and is known to have existed in the Near East following the development of herding. A Sumerian tablet dating to approximately 2,500 B.C. describes the butter-making process from the milking of cattle, and contemporary Sumerian tablets record butter as a ritual offering.
Bog butter is butter that was packed into barrels called firkins and buried in peat bogs, where the cool, airless, and acidic environment slowed spoilage while the fat aged. The practice was most common in Ireland between the 11th and 14th centuries and had ended entirely before the 19th century. The National Museum of Ireland holds examples of recovered bog butter.