Short answers, pulled from the story.
Neodymium was discovered in 1885 by the Austrian chemist Carl Auer von Welsbach in Vienna. He separated it from didymium, a substance previously believed to be a single element, using spectroscopic analysis. Pure neodymium was not isolated until 1925.
Neodymium magnets are made from the alloy Nd2Fe14B, combining neodymium, iron, and boron. They are the strongest permanent magnets known; a magnet of a few tens of grams can lift a thousand times its own weight and can snap together with enough force to break bones.
Neodymium magnets are used in microphones, professional loudspeakers, headphones, guitar pick-ups, computer hard disk drives, MRI machines, and the electric motors of hybrid and electric vehicles. Each Toyota Prius requires 1 kg of neodymium per vehicle. Wind turbines that use permanent magnet generators also depend on them.
Neodymium glass changes color because the sharp absorption bands of the Nd3+ ion interact with the emission spectra of different light sources. It appears reddish-purple under daylight or incandescent light, blue under white fluorescent lighting, and greenish under trichromatic lighting. The first commercial neodymium glass was produced by Leo Moser in November 1927.
Most of the world's commercial neodymium is mined in China, which as of 2015 holds the bulk of global production and reserves of rare-earth elements. Other mining areas include the United States, Brazil, India, Sri Lanka, and Australia. World production was about 7,000 tons in 2004.
Neodymium magnets can attract each other from large distances and snap together with great force; there is at least one documented case of a person losing a fingertip when two magnets snapped together from 50 cm away. If multiple small magnets are swallowed, they can pinch soft tissue in the gastrointestinal tract, leading to an estimated 1,700 emergency room visits and the recall of the Buckyballs toy line.