So strange!
Are you guys using an internal audio router such as Soundflower? If not then download it.
Soundflower (Mac) - Download
Once it's downloaded and installed, launch it and you should see a little flower icon appear on your taskbar next to your battery indicator.
Then go into system prefrences, select sound, then under output select "Soundflower 2ch".
Now open audacity and before you go to record, make sure and select "Soundflower 2ch" under the input source tab (toward the top of the Audacity window next to the microphone icon). Under output (just to the left of the input tab) select internal speakers or if you are using an audio interface, select it.
Now try recording and see what happens. This is exactly what I do when recording direct sources and I've never experienced these issues.
As for the iTunes question, I'm not sure. I use iTunes very casually so I don't experiment too much there unfortunately.