Short answers, pulled from the story.
The earliest reported use of a mortar occurred in Korea during a naval battle in 1413. The Korean wan'gu, or gourd-shaped mortar, dates back to 1407 and is generally credited to Ch'oe Hae-san, who lived from 1380 to 1443.
Sir Wilfred Stokes devised the Stokes mortar in 1915 during World War I. His initial design was rejected in June 1915, but was brought into production after the intervention of David Lloyd George, then Minister of Munitions, and Lieutenant Colonel J. C. Matheson of the Trench Warfare Supply Department.
The Little David, developed in the United States for World War II, and Mallet's Mortar, designed by Robert Mallet in 1857, both reached 910 mm in calibre. The largest mortar to see actual combat in modern warfare was the German Karl-Gerat at 600 mm.
A mortar fires at a high, steep parabolic trajectory that allows shells to descend almost vertically onto targets behind cover, in trenches, or in fortifications that a flat-trajectory field gun cannot reach. Modern mortars in the 60-120 mm range are also light enough to be carried by personnel without vehicle assistance, unlike howitzers and field guns.
A spigot mortar uses a solid rod over which a hollow tube built into the projectile fits, inverting the usual barrel arrangement. The propellant sits in a cavity at the top of the projectile tube, and a long firing pin runs the length of the spigot to set it off. This design allows a lighter, smaller launcher and permits ammunition of almost any weight and diameter to be fired from the same unit.
Precision-guided mortar munitions add GPS or laser guidance to standard mortar rounds. The XM395, developed by Alliant Techsystems, uses a GPS kit that replaces standard fuses on 120 mm mortar bodies. Sweden's Strix round uses an infrared imaging sensor to guide itself onto armoured vehicles and has a range extendable to 7.5 km with a sustainer motor.