Is it possible to get infected with the amoeba, Naegleria fowleri, through your ears, or is the nose the only way it can enter to cause infection? How commonly is it found in your stool as well?
Ears? No. The tympanic membrane (eardrum) is a watertight barrier between the outer ear and middle ear.
Exposure to the organism is extremely common due to its wide distribution in nature, but thus far lacks the ability to infect the body through any method other than direct contact with the olfactory nerve, which is exposed only at the extreme vertical terminus of the paranasal sinuses; the contaminated water must be deeply insufflated into the sinus cavities for transmission to occur.
In short: Don't huff warm lake water too deeply through your nose, and you'll probably never get it.
You shouldn't find it in your stool. Other amoebic infections can be found in your stool, as they can attack the lining of your intestines, but Naegleria, specifically, will reside in your sinuses and brain until you die or receive treatment.