K, I own a computer with two inputs, but only one that works. I have a Skype headset, two guitar jacks, a jack->headphone adapter, Audacity and a guitar/amp rig.

I did some test-recordings, but they were slightly complicated, with layering and ****. Because I couldn't get a monitor that didn't feedback with Audacity, I had to use guess-work for the timing of vocals, so was slightly off.

So here's my new plan. Record (with my MP3 player) a skeleton track of me singing and playing unplugged guitar. Because I managed to get a monitor working for the guitar parts, I can play them over the vocals with no problems. I can't really see any flaws with this setup, can you?

You shouldn't get feedback. Perhaps you are recording what's being played back as well. Your description of the problem isn't clear, but solving it by recording on your mp3 recorder sounds like a step in the wrong direction.

Make sure you mute the input you are recording in the playback volume control panel. That may be where the feedback is coming from.
I can't really explain it. Unless I mute all channels, the recording records everything else that I have in a new track, but really loud and fizzy, drowning out the new stuff. I can make it work with the guitar and headphones, but for some reason, not with the mic.