Short answers, pulled from the story.
The earliest known printed use of "red light district" appears in an 1894 article from the Sandusky Register, a newspaper in Sandusky, Ohio, with a prior usage in the Cincinnati Enquirer the year before. Author Paul Wellman suggested the term originated in Dodge City, Kansas, home to a well-known prostitution district that included the Red Light House saloon, though this origin has not been proven.
Red-light districts are mentioned in the 1882 minutes of a Woman's Christian Temperance Union meeting in the United States, predating the earliest known printed newspaper use of the term by over a decade.
A widespread folk etymology claims that early railroad workers carried red lanterns to brothels so their crew could find them in an emergency. Folklorist Barbara Mikkelson regards this explanation as unfounded.
Japanese police literally drew a red line on maps to indicate the boundaries of legal red-light districts, giving rise to a Japanese term meaning "red-line." A separate term meaning "blue-line" was used to indicate illegal districts.
De Wallen in the Netherlands and the Reeperbahn in Germany are among the red-light districts officially designated by authorities for legal and regulated prostitution. Some districts, including those in The Hague, operate under video surveillance to counter illegal activities such as child prostitution.
Around 1915 during World War I, brothels displayed blue lamps to indicate they served officers and red lamps to serve other ranks. This color distinction was a practical form of military-era signage.