Yes...what you described is actually harmonics(!), the high frequency component of the switching waveform prioir to the LPF is defined as harmonics.
The pulse skipping occurs if there is too much power transfer by single pulse when light loaded. The PWM cannot reduce pulse width too narrow due to circuitry so they went to pulse skipping. Try this on DC/DC with PWM and vary the load. The problem with the pulse skipping that the harmonics and fundamental shifted to lower frequnecy into audio frequnecy.
BTW, with fixed load by the speaker, pulse skipping may not likely to occurs, but when you reduce the volume to very low level, PWM generates narrow pulse width and hence more likely to pulse skips.
Generally higher freq *may* give compant circuit and perhaps reduce losses, but as the current start to increase to say 20A, the switching frequnecy may need to be reduced due to MOSFET capacitance (major losses element). It very depends on input voltage, output voltage and circuit topology.
Thank for information on core... I worked on ferrite core for specilist application involving high temperature (150 and 180degC), which is more suitable.