1) according to a report from Okinawa, a flat tire was the culprit.
2) never heard of it, happened to a collegue on take-off, he screwed up
3) use all available controls, rudder, brakes, whatever to stay on the runway
4) flap retraction is probably not a factor, unless both pilots get distracted fumbling with the flaps. Forget about the hydraulic nose wheel steering, the rudder gives you plenty directional control down to slow speed. You only use the tiller to taxi on the ramp area and to make sharp turns on the runway. If you think the hydraulics gave un-commanded nose wheel deflection which sent the airplane off the runway, you are probably wrong. (The odds are much higher that the pilots did not control the plane)