Where to report USABO Top 50 and research awards?

Last year, I scored within the Top 50 for USABO and won some major international and national research competitions.

However, I can’t find any official list of Top 50 USABO scorers, so where do I show colleges verification? Is it fine if my teacher just mentions it in her recommendation letter, since she’s also the one that handed me the certificate for my score?

For research competitions, I understand that AOs could find the information online, but is it excepted for applicants to email the admissions office with their own certificates?

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Awards that you’ve received should be listed in the Awards section of the application.

No, schools don’t expect proof of everything you’ve listed. The fact that an application can be rescinded or you can be kicked out of school later if they find you’ve lied on your application is usually enough of a deterrent that they take the provided data at face value (unless the claims are extraordinarily unlikely).