FFT results are repeating?
Interesting code! This was tough to follow from the pictures, but I did run the OP's code from the linked site, I can't play the sound loud enough to really test but appears to not be very sensitive for lower volume signals. There is no indication of the frequency axis on the graphic but I assume the left side of the screen is DC and the right side of the screen is half the sampling rate.
The sampling rate in the code was 4200 (I assume Hz) which would be way too low for audio and suggest the OP is seeing the aliasing of all higher frequencies above the Nyquist frequency of 2100 Hz. Since the audio system has a likely bandwidth of 15 KHz, any signals in multiples of 2100 Hz up through that frequency range would fold in and be a more obvious explanation of multiple frequencies due to aliasing.
I did change sampleRate to 44100 and it appeared (in my minimum ability to test) to behave more as expected.
Room echoes on their own should not be non-linear meaning they would not create new frequencies but only modify the phase and amplitude of the frequencies that already exist.