<p>Everything in your app is awesome other than your SAT score, which is quite low for any of those schools.
So here you go:
Rice: low reach
Stanford: high reach
Duke: reach
Northwestern: reach
Vanderbilt: low reach
Columbia: high reach
Princeton: high reach
Harvard: high reach
Brown (+PLME): reach
Here’s Why: harvard, stanford, columbia, princeton high reach no matter what happens. I got into Rice with worse stats than you so yeah rice and vandy should be low reach lol. Duke and northwestern are pretty hard so I just say reach, while Brown rejects people very unexpectedly (probably because it’s ivy league). There is just no such thing as a safe or even target school for schools of such caliber, they are always reach in some way. I know an alumni from our school who is pretty much the most perfect person I have ever seen, with straight A+ all four years, 5 in everything, 2390, and absolutely stellar extracurriculars at a SUPER rigorous school. She didn’t get in Harvard or Princeton, which shocked many people. On the other hand, less perfect people have gotten in those schools, indicating that getting into these schools are kind of a shot in the dark. You can never expect what happens.
In the midst of such solid application, your SAT score is quite unexpected, which admissions officer may imply that your school has grade inflation (your school’s quality actually affects your decision in a subtle way.) As for essays, you claimed that you are a great writer and your English teacher said you are one. I am a bit confused about that because you got 610 for reading. But anyways, based off of my talks with admissions officers, you SHOULDN’T be treating your college essays as English essays because you may fail it even if you are a great writer. Are you sure that you’ve got all the components that makes a good personal statement? You can be a bad writer and still have a good essay, and vice versa.
Right now I’m just picking out potential flaws though, in general your app IS solid and purts awesome. 
good luck. I think at least 95% chance you will at least get in one of them. </p>