Dual KB works pretty much as you'd expect/hope. You basically can address ONE of the 3 sections in panel B from the external keyboard, and everything else can be played from the the internal keyboard. It obeys all layers and splits (and transpose, if you ask it to) on all you play from the internal as well as the external keyboard.
So, to address your questions:
1) No, you still have the remaining 2 sections.
A) Yes, if you have one piano addressed from the external keyboard, the other is available from the NS3 keyboard (in any split/layer/transpose you want).
B) Yes, in the same condition, you have two organs from the NS3 keyboard (in any split/layer/transpose you want).
C) Yes, in the same condition, you have two synths from the NS3 keyboard (in any split/layer/transpose you want).
As to SONG mode, then @anotherscott is again correct; the Dual KB status is saved as part of the program and not the song.
Now, there is another option to consider... What about a 3 keyboard setup (or 2 keys plus a sequencer)
If you enable Dual KB, you can address any of the 3 sections in Panel B. But at the same time, you can also assign a MIDI channel to Panel B. So you could have e.g. Panel B Organ adressed by an external keyboard playing MIDI channel 16, and the Synth and Piano in Panel B split, layered and/or transposed on MIDI channel 2 from another external keyboard, and still be able to play all 3 sections of Panel A from the internal keyboard in any split/layer/transpose you like. Or you could play the other 2 sections from Panel B and assign the entire 3 sections on Panel A to be played from another board/sequencer.
So most combinations of internal/external can be catered for, it looks -- with exceptions like not being able to play 2 sections of panel B externally and the last section in panel B layered with the entire panel A internally.
I am not sure if all possible combinations of using the sustain, control pedals and bender etc will work as you may want it to, but you're off to a good start with these many options.