Concerning the perception of frequencies > 20kHz, I believe that although one cannot hear such frequencies directly, their presence could have an influence on sounds lower in frequency.
Although not directly related, owing to my age, I cannot directly hear frequencies above 10kHz, yet can 'hear' the difference to a violin playing whereby the top end is rolled off. To experience this effect, JBL produced a record called 'Sessions' as a device to demonstrate and promote their speakers.
https://images-na.ssl-images-amazon....CL._SY355_.jpg
On it there is a track (track 3 on side 2) of a violin playing, first full-range, then with high frequencies above 15kHz filtered out. The filtering then occurs at 12kHz, and finally at 10kHz. As I say, I can't hear above 10kHz, but I can hear quite distinctly when the response is rolled of at 15kHz.