Can the component AV cable and the HDMI cable mirror third party apps on TV?
Number 1 is exactly true, unless the developer chose to output the gameplay through the cable. A few games do this, but most do not.

Number 2 is exactly true.

On your last question, I'm not 100% certain and haven't tried it (I don't have the component cables). Video mirroring from the iPad 2 works with the VGA adapter, so it would likely work with the component cables, but I can't guarantee it.

Edit: Looking at the specs on Apple's site under TV &amp; Video, it seems pretty clear that component out work with the apps that do video out, but not for mirroring.