Definitions of Justice in Plato's Republic

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Plato's Republic:
What is Cephalus' definition of justice? What is Socrates' problem with Cephalus' definition? What is Polemarchus' definition of justice? How does Socrates get Polemarchus to abandon his position? Is there something to be seeing between the lines with this? (Please don't let the last question keep you from answering if you are qualified to answer the rest). Thank you.

The Republic is Plato's famous attempt to pose and answer the question of what justice is and where it might be found in the kallipolis, or the "beautiful city." Along the way Plato also expresses his opinions about education, the nature of various political systems, and the place of art, poetry and virtue in the kallipolis.
His primary concern in the Republic is to try to rebut what he considers to be a very dangerous definition of justice advanced by Thrasymachus in Book I--that justice is simply the advantage of the stronger--and replace it with one that is more to his liking. By the time Plato gets to the middle of Book IV, he has advanced his own definition. He uses the Socratic method to rebut other definitions put forward as well e.g. Cephalus and Polemarchus'

1. What is Cephalus' definition of justice?
The text is this: "Well said, Cephalus, I replied; but as concerning justice, what is it?- to speak the truth and to pay your debts-no more than this? And even to this are there not exceptions? Suppose that a friend when in his right mind has deposited arms with me and he asks for them when he is not in his right mind, ought I to give them back to him? No one would say that I ought or that I should be right in doing so, any more than they would say that I ought always to speak the truth to someone who is in his condition. You are quite right, he replied. http://www.willamette.edu/~blong/Jurisprudence/RepOutI.html

331c-d. Socrates responds in a way that at first appears pretty abrupt. He assumes that Cephalus is advancing a definition of justice here in a few words, and Socrates then states Cephalus' definition in his own words:
Justice is "speaking the truth and paying whatever debts are owed."

2. What is Socrates' problem with Cephalus' definition?
The problem S has with Cs definition is that he finds a counterexample; therefore, it is not true.
But is this a fair summary of C's definition of justice? Once S has given a definition (his specialty is to subject definitions of phenomena to critical scrutiny--the so-called "Socratic method"), he is in his element and begins to probe the meaning of the definition. He does so by asking whether you ought to return a gun to a madman if it belongs to him. Because the answer (no) immediately shows a weakness in the definition, the definition cannot be correct (331d). Instead of staying around to enter more deeply into ...