Short answers, pulled from the story.
A mineral is a solid substance with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form. The geological definition normally excludes compounds that occur only in living organisms, though substances like calcite are often biogenic.
The International Mineralogical Association recognizes 6,145 official mineral species. The IMA is the generally recognized standard body for the definition and nomenclature of mineral species.
Eight elements account for over 98 percent of the Earth's crust by weight, and in order of decreasing abundance they are oxygen, silicon, aluminium, iron, magnesium, calcium, sodium, and potassium. Oxygen composes 47 percent of the crust by weight and silicon accounts for 28 percent.
A mineral has a fairly well-defined chemical composition and specific crystal structure, while a rock is any bulk solid geologic material that is relatively homogeneous at a large enough scale. A rock may consist of one mineral or be an aggregate of two or more different minerals segregated into distinct phases.
Polymorphs are minerals that share a chemical formula but have a different crystal structure. For example, pyrite and marcasite are both iron sulfides with the formula FeS2, but pyrite is isometric while marcasite is orthorhombic, and quartz and stishovite both consist of silicon dioxide.
The Mohs hardness scale is an ordinal scale that measures a mineral's resistance to scratching, where a mineral with a higher index scratches those below it. It ranges across ten indicators from talc at 1 to diamond at 10, the hardest natural material.
The International Mineralogical Association excludes biogenic crystalline substances, which has been a topic of contention among geologists. Skinner's 2005 definition treats all solids as potential minerals and includes biominerals, of which over 60 had been discovered, named, and published before the IMA's listing.