Short answers, pulled from the story.
Calcium carbonate is a chemical compound found in rocks as the minerals calcite, aragonite, and vaterite. It occurs in limestone, chalk, marble, travertine, eggshells, gastropod shells, shellfish skeletons, and pearls, and has been detected on Mars at locations including Gusev and Huygens craters.
The three anhydrous polymorphs are calcite, aragonite, and vaterite. Calcite is the most thermodynamically stable at room temperature, aragonite is only slightly less stable, and vaterite is the least stable and its crystal structure is not fully understood.
The carbonate compensation depth is the ocean depth at which the rate of calcium carbonate precipitation equals its rate of dissolution. In modern oceans it ranges from 4,000 to 6,000 meters below the surface, varying by polymorph.
Milk-alkali syndrome is a condition caused by excessive calcium intake that can lead to hypercalcaemia, kidney failure, and alkalosis. It was first widely seen in patients following Bertram Sippy's 1915 ulcer regimen of hourly milk, cream, and alkaline powders, and since the 1990s has been most frequently reported in women taking calcium supplements above the recommended 1.2 to 1.5 grams daily.
In construction it serves as a building material, road aggregate, cement ingredient, and the source material for builders' lime. In papermaking, printing and writing paper can contain 10 to 20 percent calcium carbonate by weight, and it has replaced kaolin in glossy paper production in North America.
Water underground is exposed to carbon dioxide levels above atmospheric, which causes calcium carbonate to dissolve into it. When that water emerges and loses carbon dioxide to the air, the compound becomes less soluble and precipitates, slowly building cave formations over long periods.