The strongest essays will tell a clear story or develop an argument with evidence.
The admissions officers will be learning about you by seeing how you construct this argument or how you incorporate characters and language to tell your story.
You're applying to colleges, so you might think you should talk about yourself and your extra-curricular activities, like in a typical personal statement. It seems obvious, but be sure you're answering the essay question!
For example, if I were writing Essay Question #3, I would make sure I've answered all three parts of the question, so ultimately, the admissions officer would have an idea of what I think history is, who "they" are, and what "they" aren't telling us.
The second supplemental essay should be much easier than the first, but that doesn't mean you can slack off. Do your research and then explain why the unique aspects of the college make it your top choice.
The admissions officers read hundreds of these essays and they see many of the same responses: The Core! The college admissions website is a great place to learn more about what makes UChicago special.
If any of these interest you, explain why you think UChicago's flag grants, for example, would help you get a head start on your future research and career goals. Because you're quirky, you love to learn, you spend way too much time falling through the rabbit hole that is Wikipedia, you want to learn Econ from the masters, you...
Let your sincere feelings about the college shine through!
UChicago is looking for students who will make the college community even better than it already is.
Find UChicago-specific extracurriculars that you're interested in and explain how you would contribute to that group. Tell the admissions officers what group you think UChicago should start and how you love that UChicago lets students grow their own on-campus activities (though make sure it really doesn't already exist, because almost everything does! Research the study abroad programs, travel grants, research opportunities, and other unique programs UChicago offers.