Does multiplayer or difficulty affect the quality or quantity of loot that drops?
Loot is instanced. Each player sees only their own loot, so the general loot quantity is unaffected by playing multiplayer, regardless of how many players are playing.
Neither the number of players you have in your party or the difficulty level effects loot quality. In order to get better drops you want to be stacking magic find, and as the loot is all instanced, this will affect the loot that drops for you, rather than being split out across your party like in other games.