Yes. You can identify an animal by its feces. The amount of feces can be used to help determine the animal's size. Different types of animals have different appearing feces (eg, bird versus mammal). Microscopic and genetic testing can be done on cells found in feces to identify source.
You can identify different species of animals from one another definitely. Bear scat looks a lot different than wolf than duck etc. But individuals of the same species are a lot harder and require an intimate knowledge of the animals behaviors, diet and point in the life cycle. And even then it's not a sure bet.
Yes, to a degree, but it is unsafe due to potential disease. One can make guesses based upon location, size, and feces appearance, but without scientific analysis it is difficult.
Yes, you can identify an animal by its feces. The feces of different animals looks different ways. For example, when you see rabbit feces you are able to identify it immediately.