What are my chances at a school like Princeton?

So I’ve been browsing CC for some time and thought it was about time that I got some opinions on my own application.
If you guys have any ideas on what I can do improve, feel free to share. Now, here it goes:

SAT I (breakdown): 1600 (800 M, 800 R/W, 24 essay)
ACT (breakdown): 36 (36 E, 36 R, 36 M, 36 S)
SAT II: 800 Molecular Bio, 800 Chemistry, 800 Math I, 800 Math II, 800 US History, 800 Physics, 800 Spanish
Unweighted GPA (out of 4.0): 3.99
Weighted GPA: 4.71
Rank (percentile if rank is unavailable): 1 (at a small school of roughly 75)
AP (place score in parenthesis): Biology (5), Chemistry (4), US History (5), Macroeconomics (4), Microeconomics (5), Statistics (5), Calc AB (5), Psychology (5), English Lang (5), Human Geography (5), Environmental Science (5), European History
IB (place score in parenthesis): N/A
Senior Year Course Load: AP Spanish, Anatomy and Physiology, Nutrition, AP Lit, Gym, Medical Interventions (DCC), AP Calculus BC
Major Awards (USAMO, Intel etc.): USABO Finalist, Ranked 1st in State for Biology Science League, International Rutgers Oncology Olympiad 1st place, National Spanish Exam (Gold)

Extracurriculars (place leadership in parenthesis): Model UN (Secretary-General), Soccer (Captain), Red Cross (Founder and President), Science Bowl (Founder and President), Quiz Bowl (Founder and President), USABO Club (President), STUCO (President), Spanish Honors Society, National Honors Society, Debate Club (President), Math League, Science League, Interact, UNICEF, and Founder/Director of a Non-profit, Columbia Science Honors Program
Job/Work Experience: Summer Camp Counsellor, Tutoring, Research Internship at high ranked university, Interned at doctor’s office, Shadowed a neurosurgeon
Volunteer/Community service: 150 hours at local hospitals, 150 hours EMS, 100 Library
Summer Activities: Research Internship, Governor’s School of NJ, Volunteering, Taking College Courses
Essays (rating 1-10, details): Common App - 9, I spent a lot of time on it and felt pretty good about it overall

Recommendations:

Teacher Rec #1: Biology
Teacher Rec #2: Calculus BC Teacher - 10; I read one of the recommendations he had written for me last year for a summer program
Counselor Rec: No idea
Additional Rec: PI at the lab where I interned; well written, was impressed by my work

A couple of additional notes: I go to a magnet high school that doesn’t offer many APs and instead offers alot of dual college credit classes, so I’ve self studied for most of my exams. My school is fairly new (has only had 5-6 graduating classes), and hasn’t sent many students to ivy league school, but the five students that were accepted to schools like hopkins, yale, harvard, upenn, and cornell were all within the last year. As of now, I’m a bit worried that my ECs aren’t too strong. Any advice would be appreciated.

Wow your test scores are incredible!! Your GPA is also very strong. Even your ECs aren’t too bad either so I definitely give you a shot. But it is Princeton and even qualified students don’t get in. But you will definitely be going to a great school!

I’ve read many of these “chance me” threads, and I don’t think I’ve seen test scores as impressive as yours - top marks in everything is astonishing, and you have my jealousy. Your various volunteer/job experiences are good too, I’d wager you’ve invested more time in extracurricular activities than the average student.
My only advice would be to really focus on what you’re required to write for the common app/universal college app and for the Princeton supplement. You really have to sell yourself and make a compelling case for why Princeton should accept you.
I’m trying for Princeton too, and I wish you the best of luck!

I think you have a really good chance for top schools. I have no idea why you’re selling yourself short. Your awards and extra circulars are amazing.

Is this a joke mah dude