Dear Professor L. Mersini-Houghton,
Great thought provoking essay, I have a couple of comments/observations if you dont mind.
I would have to agree your answer to "Does the multiverse exist?" given your definition of the multiverse "contains all the universes, domains, matter and particles, energy and vacua, and any other object you can think of embedded in its spacetimes.". If the multiverse doesn't exist, where are the particles?
Regarding "If there is a multiverse, what does it look like?", you provide a significant amount of material for the reader to digest, but perhaps I am left a little confused. We all want answers, just tell us what it looks like so we dont have to think so hard about it. I am joking of course, not all question in physics have been complete answers at this time, otherwise there would be no jobs for physicists.
WRT the role of mathematics in physics, I thought your comment "can nature contain laws and axioms that cannot be written in a mathematical language, yet still exist?" provided a solid basis to think about the role of mathematics in physics.
Best of luck in the contest, and if so inclined, you can read my essay here. You will see a view of the world that quite different from yours. Regardless of the difference, I really enjoyed your essay and thought it was very well done and a pleasure to read.
Regards, Ed Unverricht