Short answers, pulled from the story.
Indirect fire is shooting a projectile at a target that cannot be seen by the aimer. NATO defines it as fire delivered at a target which cannot be seen by the aimer, with azimuth and elevation set using instrumental methods rather than direct line of sight.
Indirect fire has ancient origins, with archers and catapult crews using it in battles and sieges. The first incontrovertible documented use of modern indirect fire in war, using the geometry developed by Russian officer Lieutenant Colonel K. G. Guk, was on the 26th of October 1899 by British gunners during the Second Boer War.
Lieutenant Colonel K. G. Guk, a Russian officer, published Field Artillery Fire from Covered Positions in 1882. He described using angles to aiming points that could lie in any direction relative to the target, which became the foundation for modern indirect fire technique.
The Goertz panoramic sight was a periscopic design produced by a German firm in 1906 and adopted by both the British and the Russians. It placed the eyepiece at the rear and the rotatable top above the aimer's head, allowing the aimer to lay the gun in any direction without having to move around the weapon. The British called it the Dial Sight; the Americans called it the Panoramic Telescope.
Governor Chen Gui described using traction trebuchets to defend De'an city from 1127 to 1130 in his book City Defense Records. His method placed catapults inside the wall to conceal them, used a designated wall-observer to watch where each stone landed, and adjusted range by changing the number of pullers or moving the catapult rack.
By the end of the 20th century, the typical maximum range for the most common guns was about 24 to 30 km. This compares with roughly 8 km at the time of the First World War.