Leo says the USB headsets will make that noise over time (he calls it "cyloning"). It's a memory leak. The only way to fix it is to unplug the mic and plug it back in. Leo suggests a bad chip on the sound card is the root cause.
In Skype's audio settings he can choose where he wants the output to go. But Leo's not convinced that it wouldn't just put all of the audio into the device he selects as an output on Skype. He may need to have two sound cards to do that. The chatroom points out that if he had a USB headset, that would act as a second sound card. Then he could tell Skype to send the audio to the headset while still watching the movie on his TV through the HDMI connection.