Why does Plato employ such a complex frame to his narration of the events? Rather than simply tell the tale of Socrates' last hours, he sets it as a posthumous conversation between Phaedo and Echecrates in a remote township, while also explicitly pointing out that he, the author, was absent from Socrates' death due to illness. What effect does this have on the reader?
The main purpose of this framing device is to make clear that this is not a factual retelling of the events of Socrates' death. Plato has chosen this context to set forth his own theories about the immortality of the soul. He wants to ensure that the dialogue is not read as a narration of events but as a philosophical work, and so makes it clear that this is only his own version of an event at which he was not present. Setting the conversation between Phaedo and Echecrates serves both to reinforce Plato's desire that it should be read as philosophy, and to emphasize its importance. Phaedo and Echecrates are both philosophers themselves, so the discussion is clearly intended for a philosophical audience. Also, the fact that this story is being retold in a remote Peloponnesian town suggests the widespread importance of the subject matter being considered.
When Socrates says that objects in the world participate in the various Forms, what does he mean? In what way does a beautiful person participate in the Form of Beauty?
Plato is never very clear on what precisely he means when setting forth his Theory of Forms. There are three main readings of how something participates in a Form (as suggested in the Commentary section of 100b - 102d). First, there is the view that Forms are paradigms. Under this interpretation, the Form of Beauty is the paradigm of beauty, and a beautiful person participates in this form by imperfectly resembling the paradigm of beauty. Second, there is the view that Forms are universals. Under this interpretation, the Form of Beauty is the quality that all beautiful things share in common, that which makes them such that we can say that they are beautiful. A beautiful person would then participate in the Form of Beauty by possessing that shared quality that makes things beautiful. Third, there is the view that Forms are stuffs. Under this interpretation, the Form of Beauty is the sum total of all instances of beauty in the world, and a person would participate in the Form of Beauty by possessing some of the "stuff" that is beauty.
What role do Forms play in this dialogue, and what philosophical work do they do? In what way are they necessary for Plato's arguments? From this, what can you reasonably infer about them?
Forms are put to their most significant use in Plato's final argument for the immortality of the soul, where they are presented as teleological causes. The best reason why anything in the sensible world is the way it is will always be given through an appeal to the Forms it participates in. The Theory of Forms is the hypothesis from which all of Plato's arguments follow, and itself is taken for granted. Thus, Forms serve as the ground for everything Plato says, and must then necessarily imply the Theory of Recollection and the immortality of the soul. In spite of all this, it is very difficult to determine precisely what we should say about Forms. (this dialogue's Commentary sections provide only hints toward several different possible answers.