There's always a couple of choices of take off flap available. More flap will give a shorter run, but worse overall climb gradient, whilst less flap gives a better gradient but longer take off roll. In the A380 we can use 1(+F), 2, and 3 for take off, and all are reqularly used.
On your 747 departure, you would most likely have used flap 20, which is the usual take off setting. Full flap is 30, and it is never used for take off. Nor is 25. If I recall correctly, the settings are 0, 1, 5, 10, 20, 25, 30...so a multi stage retraction is quite normal.
Picking thrust changes, and the reasons for them, from the cabin is a difficult exercise. You would have taken off at a derate, that would have been held until the clean up height at which point the thrust would have change to one of the climb thrust modes. Out of JFK there are multiple inbound traffic lanes to be avoided, and they would have constrained the climb. Speed is limited to 250kias. All sounds like a normal day.
