It's "Turn My Way" by New Order, off their 2nd to last album, "Get Ready" from 2001. Billy does mostly backing vocals except a few select parts of the song. After hearing "Turn My Way", I checked out the rest of the album back then, and thought it was great, so I asked for it as a gift for the holidays I believe or perhaps my birthday, depending on when the exact release date was. Anyways, great album
"Thwart the Ends" is actually "Never Ever" by James Iha, which appears on some compilation in a Japanese music magazine or something like that. That was at least 4 years ago I think though.
Sounds like the other fake tracks are actually Djali Zwan songs from the Spun soundtrack.