I’ve written a scientific paper in high school (currently in pre-print) & also have designed an experiment. I have acted as a trainer for the Asian Physics Olympiad 2016 team & was a team member in both previous year’s APhO & IPhO but failed to get an award :/ I am curious if any of these accomplishments will help my chances in top Ivy schools, and if so, how. My personal dream school is Yale.
Those achievements will definitely improve your chances of acceptance at top schools. All of these activities indicate that you're passionate about science and are already focused on making meaningful contributions to the field. Even though you didn't win an award in the Asian Physics Olympiad, it's great that you've contributed to the team consistently over the course of your time in high school. That shows dedication and a genuine love of learning. Here's a quote from Yale's admissions website on what they look for:
As we carefully and respectfully review every application, two questions guide our admissions team: “Who is likely to make the most of Yale’s resources?” and “Who will contribute most significantly to the Yale community?”
It appears that you've managed to make the most of the resources available at your high school, so you've already shown yourself to be a promising candidate. Of course, your chances of being accepted to a school like Yale also depend heavily on your grades and test scores, but the activities and achievements you mention here should do quite a bit to improve your odds.