The answer to your first question is contained in the second question you ask. Miss Emily had been one of those "women of the Old South," from a family of means, and is now in a position where she isunable to pay her taxes or maintain her household properly. Do you see the idea behind a person on a pedestal and a fallen monument? A person who has toppled from the pedestal is a kind of fallen monument. If you try to combine thes ideas, you get a bit of a mixed metaphor because a statue is not exactly the same as a monument, but the similarity is there, something that was high and mighty has now fallen.
Why have the high and mighty fallen? It is likely that Miss Emily's family has been going downhill since the Civil War. Most of the status and wealth of Southern families was built upon the free labor of slaves. Once slavery ended, there was no free labor, and that wealth and status crumbled.
Unfortunately, many Southern families continued to perceive themselves to be above others, and consequently, did little or nothing to solve their real problem, which was to find a way to make a living without profiting from the free toil of African-Americans.
Miss Emily is likely to think of herself as still on the pedestal, or, even if she does not, the habits of generations of her family and the influence of a clearly dominating father keep her firmly fixed on the pedestal in her own mind. There is no one suitable for her to marry, and her father appears to have chased off all suitors, either because they were unsuitable or because he wanted her to take care of him.
All of these dynamics lead to a sad life and death for Miss Emily, which should suggest to all of us that when things change, so should we! That is just one message one might take from the story, but the story is rich in meaning, and there are many themes to explore.