Learn English – What are the differences of meaning between device, gadget, gimmick, and gizmo

The concept of allegory you are talking about is called personification and has been mainly used in literature in medieval times and the baroque.

There are other types of allegories, like in the Hebrew Bible, let's say Psalm 80, talking about the vine that stands for Israel. Things, as the vine, and actions can be allegorical.

In arts there are many allegorical pictures. A personification would be Justice as a blindfolded woman with scales.

Fables are a subcategory of allegories, as are parables. Both probably are characterized by shortness.

All three categories are forms of writing, art, or spoken utterance that encourage readers to look for meanings beyond what is said.

As for the difference between fable and parable: the fable, as the OP says, has animals, plants, or objects acting. It therefore has to anthropomorphize, while a parable draws its images from human interaction mostly.

Therefore a fable most the time is more schematic in build and easier to decipher. Parables often allow for different ways of deciphering. Looking at Kafka, Brecht, or biblical parables, it is clear that there is often a key, hint, or explanation needed to decipher the parable.

This might be because a fable describes something that is naturally not possible, as the actors are anthropomorphized, creating its moral effect using striking simplification, while the parable describes a naturally possible incident, allowing for more complexity due to acquaintance, creating its moral or parabolic effect through surprise. Fable and parable therefore have much in common and overlap greatly.

The three prepositions imply three different things:

For emphasizes the employer-employee relationship. If I work for a company, they issue my paycheck, and they can fire me for poor performance.

At emphasizes the locale where I work. If I work at a company, I usually park in their parking lot, and work in their building each workday.

With emphasizes that I'm part of a team. If I work with a company, then that company's workers are my co-workers.

The words are essentially interchangeable in many contexts, because many of us do all three at the three time. If I was employed at Nike, for example, I could say that I work for Nike (they issue my paycheck), at Nike (I work in their building), and with Nike (I work with their employees). Quite often, saying one implies the other two.

One of the three prepositions may become less appropriate if one of those three conditions isn't true. If Nike hires me as an independent consultant or specialist, and they allow to me work from home, I might be less prone to use at. If I serve on an advisory board in a part-time, volunteer capacity, I might be more inclined to use with, and less inclined to use for.