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Because the 5D II will only trigger the 600 using optical mode (not radio), I think you will need to use that with the 5D III as well. The off camera flash should respond to both on camera flashes as long as they're in the same trigger mode.
I don't think that's correct . You can master/slave with radio on older bodies . The max sync speed may be slower though (although I think canon have been a bit conservative in saying that as many report sync at max sync speed )