Short answers, pulled from the story.
The first recorded stagecoach route in Britain started in 1610 and ran between Edinburgh and Leith. By the mid-17th century, a basic stagecoach infrastructure had been established across England, with routes connecting major cities.
John Palmer proposed in 1782 that the Post Office adopt stagecoaches for mail delivery, replacing the slow system of mounted postal riders in use since 1635. His experimental run from Bristol to London on the 2nd of August 1784 completed the journey in 16 hours, compared to the 38 hours the old system required. By 1797 the network he created had grown to forty-two routes.
The Concord stagecoach, first built in 1827 by two men in Concord, New Hampshire, suspended its body on long leather straps rather than rigid metal springs. This gave a swinging motion that was far more comfortable on rough American roads than European-style iron-spring coaches, which wore out quickly. Mark Twain described it in his 1872 book Roughing It as "an imposing cradle on wheels".
Railway competition from the late 1830s ended stagecoach service on most main routes. The first rail delivery between Liverpool and Manchester took place on the 11th of November 1830, and by the early 1840s most London-based coaches had been withdrawn. Transcontinental staging in the United States ended with the completion of the transcontinental railroad in 1869.
The phrase derives from the armed guard who sat beside the stagecoach driver, carrying a coach gun to protect against robbers. Postal riders on the pre-stagecoach system were frequent robbery targets, and the armed messenger became a standard feature on many stagecoach routes.
Stagecoaches in Victorian Britain were taxed on the number of licensed passenger seats. On the London to Newcastle route of 278 miles, the annual passenger seat tax came to £2,529 for a coach carrying 15 passengers. Annual road tolls on the same route added £2,537. Operators who ran six days a week instead of seven could reduce their tax burden by one seventh.