Short answers, pulled from the story.
An emerald is a gemstone and a green variety of the mineral beryl, with the formula Be3Al2(SiO3)6. Its green color comes from trace amounts of chromium or sometimes vanadium, with iron acting as a third color-determining trace element.
Emerald has a hardness of 7.5 to 8 on the Mohs scale, so it resists scratching well. Its toughness, meaning resistance to breakage, is classified as generally poor because most emeralds contain many inclusions.
Most emeralds are oiled to fill surface-reaching cracks and improve apparent clarity and stability, since stones without fissures are extremely rare. Cedar oil is common because its refractive index is similar to the stone, and the U.S. Federal Trade Commission requires sellers to disclose oil treatment.
Colombia is historically the world's largest emerald producer, accounting for 47 percent of global output in the decade leading up to 2005, with main areas at Muzo, Coscuez and Chivor. Zambia is the second biggest producer, and emeralds were mined in Ancient Egypt at Mount Smaragdus from 1500 BC.
Synthetic emeralds are produced by flux-growth and hydrothermal methods. Carroll Chatham ran the first commercially successful synthesis using a likely lithium vanadate flux, Pierre Gilson Sr. grew flux emeralds on beryl seeds at 1 millimeter per month, and Tairus is the largest hydrothermal producer today.
Notable emeralds include the Bahia Emerald from Brazil at 180,000 carats, the Zambian Chipembele at 7,525 carats found in 2021, and Colombia's Duke of Devonshire Emerald at 1,383.93 carats. The Mogul Mughal Emerald, inscribed with the year 1107 A.H., is held at the Museum of Islamic Art in Doha.
Emerald is the traditional birthstone for May and the gemstone of the astrological sign Taurus. Alchemical lore held it counteracts poison, and Hernan Cortes had a looted Mexican emerald engraved with a line from Matthew 11:11, while L. Frank Baum's 1900 novel The Wonderful Wizard of Oz features an Emerald City.