thinking about sending it in to Rick Riordan when it is finished.
Don't do that. Authors never want to see work by unpublished authors, and even if they did, there's nothing they could do about it.
On the story, I wouldn't start with a dream sequence. Readers hate dream sequences. Also, don't say things like "he responded" or "he stated". Just "he said" is fine. Look carefully at some dialogue in novels you like and study the way speech is presented there. Otherwise, a good start!