Knowledge of what? This is a pretty broad way to start a poem, isn't it? Perhaps, by opening with such a general idea, Dove is indicating that she wants knowledge for everyone. After all, couldn't everyone use a little knowledge?
To understand each desire has an edge, (2)
It's not enough just to understand your desire; you have to understand what it will cost. That's the "edge." Hades acted without considering what this cost might be. Demeter wants him to think before he acts, next time. Unfortunately, for Demeter and Persephone, the damage has already been done. Maybe this knowledge will be helpful to someone who hasn't made a selfish mistake like Hades did. Maybe this isn't so much a prayer as a warning.
There are no curses—only mirrors held up to the souls of gods and mortals. (23-24)
The only real curse, she says, is to be face-to-face with yourself. Say what? Demeter says that facing up to our mistakes is punishment enough. In order to own up to your mistakes, though, you have to know that you did something wrong in the first place. That's the knowledge she wishes on Hades. Whether he gains that knowledge, though, is another story.