To me, it seems they make very inefficient use of their existing runways. I normally depart ICN between 20:00 and 21:30. There's very frequently a significant backup of planes waiting to depart during that time, and sometimes our plane will wait 30 minutes or more at the gate waiting for a departure slot. But the third runway, AFAIK, is just idle during that time. I don't know anything about runway operations or the specifics at ICN, but seems to me they really need that third runway operating during that time period.

I think for departures, KE and OZ have their peak departure times in the evening, though in the early morning there's another peak. For arrivals though, I think it peaks in the early morning for all airlines, KE, OZ, and foreign, because there's a huge number of red-eyes that arrive at that time. There's no public transportation before roughly 05:00, so all the airlines want to arrive between 05:00 and 07:00. It's been during that time when actually I arrived at a main terminal gate on one of my TG flights, I'm assuming because all the gates at the concourse were occupied. So while the capacity has not yet been reached overall, I think it already has been reached during these peak times we're talking about. Still though, the airport operates extremely efficiently even at peak capacity. Outbound waits are never too long at security/immigration, and there never seems to be any problems at check-in that I can see. The OZ business class lounge can get overcrowded from what I've seen, but I don't know about the KE lounges.

If I'm reading the map of the airport expansion right, the new terminal will be built in two different phases, with half of it completed in Phase 3 and the remainder in Phase 4. If that's the case, I don't know that half of the terminal would be big enough for KE, but it certainly would be big enough for OZ.