To find wildlife, your best bet is to be in a chunk in which no-one has been building. This can sometimes be a bit hard to judge but a good way is to use the Tectonicus map set to night and look for torches. Since passive mobs don't despawn/respawn, once they are gone, they are gone. However, other players are often willing to give you some of their stock for you to start a farm.
As for chests, in the spawn building, as people have pointed out, they are community stocks. Outside of the spawn building, all chests and buildings should be regarded as owned, unless marked otherwise. The chests in the village in the Wild West follow the Wild West rules (The Wild West pvp region on Frontier