How we cite our quotes: Stephanus pagination (the standardized way in which every text of Plato is divided). Every edition and translation will have this pagination in the margins.
Quote #7
"[Men trapped in the cave] would hold that the truth is nothing other than the shadows of artificial things." (515c)
In his famous Allegory of the Cave, Socrates suggests that the world we see every day is more like shadows on a wall than reality. If all you ever see is shadows on a wall, you'll think that those shadows are reality. You'd never suspect the real world outside the cave. Socrates thinks that's the way most of us live our lives: we think we're living in reality, but there's another, more "real" reality out there that we have to search for.
Quote #8
"Therefore, the real tyrant is... in truth a real slave to the greatest fawning... and with his desires getting no kind of satisfaction, he shows that he is most in need of the most things and poor in truth..." (579d-e)
"Poor in truth" means that you basically don't have any truth. You may have a lot of money and stuff, but you've got nothing real. It's a compelling way of describing the plight of the tyrant. What would you do if you led a life without truth of any kind?
Quote #9
"...it's plain to everyone that the [rational part of the soul] with which we learn is always entirely directed toward knowing the truth." (581b)
The whole truth and nothing but the truth is what the rational part of the soul is all about. And since that the part of the soul is—or should be—responsible for making decisions, well, that makes a lot of sense.