Dear Mr. Suzanne,
1. the work appears to be a dialogue, wearing the mask or thaumatopoioi of a dialogue, but is indeed a monologue like the Apology. Socrates alone speaks. But to whom? For what reason? Is he addressing the gods? Other Athenians? Future generations? I think that the the monologue quality of the work is explained to some degree at the end of the text when Socrates says that through Justice we will be "friends to ourselves and to the gods." This seems to indicate that all of the above are true.
2. The connection to other mythological works (Odyssey, Orpheus) seems to be intentional as well. Socrates goes "down into Hades" when he goes into Piraeus. The opinions of men like Thrasymachus, Polemarchus, and Cephalus being the opinions of the underworld; the world of claustrophobic materialism and almost petty worldliness. The person they most effect is Glaucon, the Eurydice character, whose trepidation that there is anything beyond this world (and thus any point to striving for greatness rather than grasping at power or pleasure) indicates that he is dead or near dead in soul. Socrates, like Odysseus, attempts three times to clasp him to his breast (by defeating the arguments of Cephalus, Polemarchus and Thrasymachus) and still Glaucon fades into that other world of sorrow and hopelessness. If, then, a man is to effect any change for the positive, he must regain a vision of the light, of greatness, and of his own immortal significance (an event that occurs to Glaucon in Book 10). If he does regain such a vision then he can effect great change for the good in the world - be remembered - and have his tale, the story of his life, saved as an individual rather than lost in the oblivion of the faceless mob.