I gave the following answers to the essay questions. (For my own vanity, I have edited some grammatical mistakes I found only after hitting submit.)
To the best of your understanding, and in your own words, please explain what “evolution” means
The theory of evolution is the common name for two theories: The theory of natural selection and the theory of common descent.
The theory of natural selection is the idea that from a large population of individuals in a species that those with beneficial variance will tend to reproduce more. This theory depended on the existence heredity for passing on traits to subsequent generations. The selected individuals would thus tend to pass on their traits more successfully and begin to alter the makeup of the population at large.
The theory of common descent is the idea that all living creatures are descended from an initial creature or population of creatures. This proposition is difficult to prove and much less intuitive. In order to prove it, a more robust theory of heredity needed to be provided.
If you accept the theory of evolution, please explain in your own words why; or if you do not accept the theory of evolution, please explain in your own words why not.
For what I understand, the theory of natural selection has become far more complicated and nuanced. So in a way I don't accept the theory of natural selection as originally proposed. I accept the refined, modern model of selection.
However, the theory of common descent has only become stronger with the gathering of more evidence. Personally though, I find the evidence that was most convincing was the evidence from animal husbandry among non-extinct species. This is the evidence that Darwin hammers upon most fervently in his Origin of Species. Try as they might, creationists, or less honestly intelligent design proponents, have little fulfilling explanation to counter the intuitiveness of arbitrary similarities.
Sure, they fall back on "Same designer, same design" but that hardly works to explain arbitrary similarities in disparate species while also accounting for independent evolution of similar structures fulfillingly.