Yes, as long as the display is on or the LED is pulsing it's on the network.

It goes to sleep after the x minute standby timer expires. Not sure what happens if you're doing a sync at the time - I suspect it still turns off. Maybe there should be a backoff timer for this!

WOL won't work in sleep, no. Even the ethernet controller is off to minimise power consumption (eg, it might be left in a long-term airport carpark)

Hugo