Wow, thanks for even including me in that amazing group of posters, I am just trying to keep up with them most of the time. 
Anyway, I too would question AP Statistics as your senior year math when you are looking at those majors. I have a future non-STEM major that may take AP Stats instead of AP Calc, but she is pure liberal arts, not majoring in Computational Math/Math/Physics. Does your school not offer a higher level Calc you haven’t taken, or Differential Equations?
14 years in Taekwondo will be looked at favorably both as a long term commitment and something where you have obviously progressed and advanced.
Avoid watering your application down with too many filler type things and try to put together a cohesive package with things that meant a lot to you include the things you learned a lot from. When you can show/describe activities that influenced you and describe how they shaped you into the person you are (through essays or activity description) that is way more impressive than listing 600 generic community service hours. That makes the reader have questions rather than answers and you don’t want to do that.
Discover Engineering will be good because it may excite you even more about USC and that will be reflected in your app. Uncle and daughter - my guess is everyone is six degrees from someone at USC, so don’t see that doing much.
If I think of anything else, will reply again later - good luck, you will have a great application, but when it comes to USC, always have a B plan. Heck, I would even tell Gandhi the same thing, they can be a bit unpredictable with their holistic review!