To echo what people have said:

1) It's the entire one way direction.
2) You can choose to, say, apply it to a single sector so that, in your case you could have it apply to JFK-NRT only so that if that failed to clear you wouldn't waste an entire GUC on just NRT to SIN.
3) I've had GRU-ATL-SEA clear on GRU-ATL but waitlist on ATL-SEA and then had ATL-SEA clear separately.
4) I've currently got a GUC applied to just LAX-SYD on a SEA-LAX-SYD ticket so that either I keep the GUC or I get to sleep on the way to SYD. (I'm assuming SEA-LAX will upgrade, if not, then I can cope on a short flight).

The thing I'm not sure is if say, JFK-NRT clears then can you call up ask that NRT-SIN is applied against the GUC as well.