You may want to provide more information in some of your questions. For example;
Is knowledge "natural"? Compare Plato or Aristotle with one of the
other philosophical approaches to this question we have considered.
What are the other philosophical approaches you have study? You would have to give a few to put this question in context. The same goes for;
Does teleology matter? Why or why not?
How would Plato or Aristotle criticize Lucretius's conception of both
nature and the soul?
As for some of the other questions,
What are the advantages and disadvantages of Plato's insistence that
the Forms are transcendent and not immanent to the natural world?
Plato's theory of forms is considered on two different but asymmetric levels in one archetype of reality. On the one hand you have a distinct individual
material things which people occupy themselves with and are considered part of our "sensible" version of reality. On a separate, some would say higher, level are entities (note that this is much like the Leibnizian concept of entelochies (monads) rather than pre-existing individual incorporeal forms) that are a) immaterial, b)intelligible. The important thing to remebr is that these higher forms are encountered only through thought and not through sensation. Think of rationalist principles and a-priori dogmatisms. The nature of these forms is a) one, b) the same as itself, c) unchanging, d) eternal, etc. But in all of this, the form represent an object of true
So when you ask what are the advantages and disadvantages of Plato's transcendent forms, you could say that there is an advantage as far as describing a causal
factor in Plato's philosophy. This is a theme revisited in Spinoza and Leibniz in regards to the principle of sufficient reason (i.e. Spinoza and the PSR of there being a single monistic world and Leibniz and his plurality of substances of which God chooses the best of all possible worlds.) But besides this point, there are other advantages. Forms are in a way models, or sources which reflect the true object best in all possible worlds. They are therefore the best type of thing in existence. The forms also represent forms of true thought
beyond our sensory experiences. So I would suggest that Platos forms offer answers to epistemological as well as metaphysical questions. But there is more to this question than this, but I am not sure what your teacher covered.
In what ways do the philosophies of Heraclitus and Parmenides set the
stage for the philosophers that succeeded them?
Heraclitus is classified into the Ionian "natural philosophers." Heraclitus for example is primarily concerned with cosmic processes and the nature of things. In fact Heraclitus is attributed the fact that he started the whole classical philosophical discourse beyond the previous attempt of Hesoid, etc. Heraclitus, to point, states that he "marks off each thing according to its nature, pointing out how it is." But the main thing to take away is that Heraclitus is most of all reformulating the cosmological analysis of the universe compared to guys like Hesiod, who relied on a very heavy cosmogony to answer the basic questions of nature. Parmendies, who had a much more different standpoint which denied plurality and change is in many ways the equal in Heraclitus because both these two philosophers are confronting the empirical cosmogony of Hesiod and those who preceded him. First and foremost, they in fact question the standard practice of cosmology. Aristotle said it himself in Metaphysics
book alpha 1, that philosophers like Heraclitus, though they did not get it right, were worthy of admiration because the stepped out side the box and thought in an asymmetric manner. They challenged the pseudo-empirical though processes of cosmogony and established philosophical thought and doctrine.