Azureth

Chosen answer: The series followed on from the original script that Joss Whedon wrote, which was in turn radically different to the movie that was released - thus numerous references to Buffy burning down a building at her old school, which never happened in the movie. Basically, the only story that follows over is this: Buffy was a student at Hemory High, quite popular (she compares herself to Cordelia) until Merrick, her first Watcher, discovered her and told her her destiny. While fighting a group of vampires, Merrick ended up dead (according to Whedon, he was trapped by a group of them and was forced to kill himself to avoid being turned); Buffy later trapped the vampires in the school gym and burned it to the ground, resulting in her expulsion from Hemory and her move to Sunnydale.

Shay

Chosen answer: Several factors restrict the demons besides the Slayer. The Watchers' Council is obviously much larger than it would need to be to simply guide the Slayer; much of their energy is directed toward gathering information for their own use against the demons. They have elite teams (seen in season 3) for Special Forces-style offensives. There are also innumerable witches and warlocks around the world, some of whom fight for good (like Giles' coven from the end of season 6) and all of whom would be attracted to the energies of the Hellmouth. Some demons like Whistler (end of season 2) exist to balance the forces of darkness with the forces of good and would handle their share as well. The existence of The Initiative (season 4) shows that the world's powerful elite are aware of the demon world to some extent and take measures to address it. Lastly, there are always some civilians who take part in the battle because they become aware of the existence of demons, like Kain from "Phases", Gunn's gang from Angel, and Wood from season 7. Obviously, there's a whole lot more than just the Slayer defending the world, but no one else can really match her firepower.

Phoenix

Chosen answer: From what we see in the series, certain girls are identifiable as potential Slayers - Kendra clearly fell into this category. The identification method is presumably mystical in nature, but the Watchers' Council are pretty effective at that sort of thing, so they're quite good at tracking down the potentials ahead of time. Not perfect, though - it does appear that Buffy herself may have slipped through the net - certainly she had no inkling of what she was until she'd already taken on the role of Slayer. It is possible, however, that this was actually cultural - an American family would hardly be likely to turn over their daughter to some strange man for 'training', so the Watchers might have chosen to keep an eye on her covertly, whereas some other cultures (like Kendra's Jamaican parents) might be more willing to believe.

Tailkinker ★