Short answers, pulled from the story.
Fire is the rapid oxidation of a fuel in the exothermic chemical process of combustion, releasing heat, light, and various reaction products. The visible flame appears once the fuel reaches its ignition point temperature, and if hot enough the gases can become ionized into plasma.
The fire tetrahedron is the set of conditions a fire requires: flammable or combustible material, a sufficient quantity of an oxidizer such as oxygen, a heat source above the fuel mix's flash point, and a sustained chain reaction of rapid oxidation. Fire cannot exist unless all of these are present in the right proportions, and removing any one element extinguishes it.
Antoine Lavoisier demonstrated that combustion did not release a substance but rather took one up, overturning the earlier phlogiston theory. In 1777 he proposed a new theory of combustion based on a material reacting with a component of air, which he termed oxygene, and by 1791 his concepts had been widely adopted and phlogiston theory rejected.
Fire was the basis of all early thermal weapons, including incendiary devices, heated projectiles, and smoke, and the Byzantine fleet used Greek fire against ships and men. The fire lance flame-thrower dates to around 1000 CE, modern flamethrowers were first used by German troops near Verdun in February 1915, and incendiary bombs caused deliberate firestorms over Hamburg and Dresden in the Second World War.
In normal gravity, convection makes soot rise so a flame becomes yellow and elongated, but in microgravity convection no longer occurs and the flame becomes spherical, bluer, and more efficient. NASA experiments revealed that diffusion flames in microgravity oxidize more of their soot than flames on Earth, with potential applications for fuel efficiency.
Studies have found that functioning smoke detectors reduce the risk of death in a fire by 50%, and sprinkler systems can reduce mortality by 100%. In the United States the leading cause of residential fires is cooking equipment left unattended, and the adoption of fire-safe cigarettes has been associated with a 45% reduction in cigarette-caused fires.
Every natural ecosystem on land has its own fire regime, and fire creates a mosaic of habitat patches at different stages of succession that lets more species coexist. Fire can stimulate plant growth and maintain ecological balance, but burning vegetation releases nitrogen into the atmosphere and produces a long-term reduction in soil fertility that nitrogen-fixing plants like clover, peas, and beans can recover.