Short answers, pulled from the story.
The Dungeon Master controls all aspects of a D&D game except the actions of the player characters. The DM describes what players perceive in the fictional world, creates or adapts the adventure scenario, enforces and modifies the rules, and adjudicates the outcomes of player decisions.
The title Dungeon Master was introduced in 1975 in Blackmoor, the second supplement to the original Dungeons and Dragons rules. It was invented by Tactical Studies Rules, the company known as TSR.
Since the launch of Advanced Dungeons and Dragons in 1977, the three core hardbound books for the Dungeon Master have been the Player's Handbook, the Dungeon Master's Guide, and the Monster Manual. Other rulebooks exist but are not required to run the game.
Other publishers use alternative titles to avoid infringing the Dungeon Master trademark held by TSR, and to describe referees in genres beyond sword-and-sorcery. Common alternatives include Game Master, Judge, Referee, and Storyteller. Call of Cthulhu uses Keeper of Arcane Lore, and Nobilis uses Hollyhock God.
Yes. The Dungeon Master is free to modify, remove, or create entirely new rules to fit the current campaign. The rules are intended to provide a balanced environment, but the DM may override them when situations arise that the rules do not cover or where they produce unintended consequences.
Yes. In the sourcebook Faiths and Pantheons, the Faerunian Overgod Ao is described as answering to a superior entity insinuated to be the Dungeon Master itself. This makes the game referee a part of the in-world cosmology of the Faerun setting.