3. Morals are the signature characteristics of fables. Fables were made to teach, instruct, provide a set of rules, not to amuse. One of the oldest known collections of fables comes from India and it is called Panchatantra.
Panchatantra stories were supposedly created by wise brahmin who was asked to teach three sons of a king at least something useful (they were spoiled and dull).
So brahmin created series of short stories featuring animals with human characteristics. These animals were set in different situations and their actions and reactions are providing examples from real life situations which can be helpful to future kings.
This story is very probably only a story (kind of fable, really) and it is great example of frame story serving to connect very different stories into more unified collection (most famous example of framed format of story telling which also includes many fables, is of course Arabian Nights or 1001 Nights).
4. As we can see the moral of the fable is presented through allegory. This means some important, in most cases abstract idea, message or moral, is represented through simple, easy to understand action with simple, one-dimensional characters. Most popular example of allegories is collection of Aesop's fables, but we can find many more examples in literature (Lord of the Flies is an allegory on human mind and civilization, Narnia series on stories from Bible, Animal Farm on social order in Soviet Union and so on), but also in other media.