What happens to the country in this story? How do Prince Prospero's reactions to these events reveal his character?

What happens is revealed in the very first lines of the story:

The'Red Death' had long devastated the country. No pestilence had ever been so fatal, or so hideous. Blood was its Avatar and its seal—the redness and the horror of blood.

So, the country is being torn apart by a terrible disease. It kills so quickly, one can assume businesses are failing, fields are remaining unharvested, and people are panicking uncontrollably. It's really quite a disturbing beginning to a story-the audience is instantly, figuratively drenched in blood.

In the midst of this assumed panic, Prince Prospero devises a terrific plan (so he thinks) to save himself. He takes "a thousand hale and light-hearted friends" and locks everyone up in his "castellated abbey", where they believe they will be safe from the plague. They shut and weld the doors, making sure no one can enter & no one can leave. This suggests that he is afraid of death, & will go to great lengths to avoid it. Of course, this is impossible, but he doesn't realize that just yet.

In addition to hiding in his castle, the prince offers amazing entertainment for his guests. It's not enough to escape the disease, they must escape it in style. So, he throws a party. It's the wildest masquerade anyone had ever been to, & every imaginable creation is represented in the costumes. At this point, it is also hinted that the prince may be slightly mad:

The tastes of the duke were peculiar. He had a fine eye for colors and effects. He disregarded the decora of mere fashion. His plans were bold and fiery, and his conceptions glowed with barbaric lustre. There are some who would have thought him mad. His followers felt that he was not. It was necessary to hear and see and touch him to be sure that he was not.

Whether he is psychologically unstable or not, he is certainly heartless, careless, cruel, and indifferent to the suffering of his subjects. Not exactly the qualities most people look for in a leader. Indeed, if one reads this as a moral tale, Prince Prospero's uncaring & frivolous attitude leads to his own death, & the deaths of his thousand guests.