Many animals get to evacuate body waste everywhere and anywhere they like because unlike us they do not have toilets built for them and are not used to using toilets.
answer 2 Not everywhere are waste practices as well organized as they are in the west. Indeed even in the west, it is not universal to put sewage through a proper three stage process. Of straining and comminution (grinding), anaerobic digestion, and aerobic digestion. These last two help get rid of these two main types of bacteria.
In some island communities, the toilets are just extended out over the sea!. In some poor cities in the world, you may find sewage just flowing down the street or alley. And in Europe a couple of hundred years ago this practice as common as well.
(Quadruped) Animals do not all exhibit a single behaviour. Indeed, the casual dropping of faeces may be peculiar to the herbivores. You might wish to check that.
Cats always cover their scat, and dogs will not evacuate themselves on their home territory.