Small update: The ethernet driver worked, thanks a lot! The MAC defaulted to 00:00:00:00:00:00 though, so I had to set it manually.
I don't know why, but sleep also works now. Maybe it's because of something I did while getting rid of the App Store "Unknown Error".
Does audio work? - YES
Does HDMI work? - YES
Does HDMI Audio work? - YES
Sleep works, that's confirm - YES
Does it sleep and wake when closing and opening lid? - Closing: YES*, opening: NO
Screen brightness is controlled by Fn+Pause and Fn+F3 or Fn+up and down button - YES
Audio control is by the right side - YES
Keyboard backlit is controlled by Fn+right arrow - YES, it's a hardware feature though
Screen snapshot is by Fn+PrintScrn - YES
Fn+F1 for sleep - YES*
tab power button to wake - YES
wireless card - NO, BCM94322 already ordered
ethernet - YES
* only after putting it to sleep manually for the first time
The very last minor thing that's missing is multitouch (at least two-finger scroll) on the Alps DualPoint touchpad. Is it supported at all? All in all, looks like the E5420 is a great base for a Hackintosh.