Why do champions respawn? How do they change looks? What is summoner's rift? The answer is Amumu.
http://i.imgur.com/9BBkljM.png
The League of Legends is in reality a dream world that Amumu, so desperate for friends, created. Every night he cries himself to sleep, and every night he finds solace in his dreams; a place where he is a champion of justice, where he fights alongside other champions, all of them based off characters he has met or heard about in his travels around Runeterra searching for friends. The majority are representations of those who have become real living Legends because of their exploits in the Great Rune War, a conflict between the different city states of Valoran; Garen of Demacia, Darius of Noxus, Tristana of Bandle City. Others like Skarner are based on mostly forgotten legends, one of the many sapient species of so long ago that no one remembers how they once populated the entire desert of Shurima. Some like Rammus and Malphite are Amumu's creations - champion versions of the many vast non-sentient creatures located within Runeterra that he had once miserably failed at trying to befriend.
Sometimes when he eats too much before nighttime, his dreams get a little wonky, and the champions show up with a different appearance. and even famous heroes of the land known for their seriousness appear with revealing or silly attire.
While Amumu will occasionally have nightmares of a dark and sinister forest, The Twisted Treeline, reminding him of his troubled journey through the Shadow Isles, he also has dreams of the Howling Abyss, the great bridge that he once visited while in the Freljord, and when he goes to sleep with nostalgic thoughts of home he dreams of the Crystal Scar. But mostly he dreams of the Summoner's Rift, his idealized version of forest paradise where he summons his friends, fighting together as champions and legends.
This would explain why heroes can flash and teleport, recall, respawn, why there are weird things like Rammus mixed in among the "serious" lore of Noxus and Demacia, and skins. It's all Amumu's fault.
, where he had disintegrated all champions in Runeterra (fo' science, yo) and the whole game is just Vel'koz calculating how different champions would have reacted in different situations, like testing grounds, but in his brain.
