From my second look experience, I think it is hard to generalize the students at Pritzker. For a small class of 88 there was an impressive amount of obvious diversity in personality and experiences. Though I honestly think most schools are like this and is not something unique to Pritzker. At this stage, for fit, I would worry about resources of the school(and possibly the schools values as evidenced by their programs or other things they tout).
With regards to the essays, there is definitely a fine line to walk between talking too much about yourself and just discussing irrelevant experiences. I liked to start off direct(something like "XXXX is the perspective I am going to bring...") and then talk about experiences regarding this perspective, eventually returning to something a little more direct. I am sure there are 10,000,000 ways to approach these questions, my way is just one option.
This may not apply to you, but I think most people are more "diverse" than they give themselves credit for.