3) is wrong. The amplifiers are powered by DC, but one side of the fiber provides positive voltage and the other negative - the ocean is not a part of the circuit.
I was under the impression that cable systems are best understood as constant-current systems. As a side effect of this, they can withstand a power failure at either end, in which case the ground path is part of the circuit. (Essentially "single rail" operation.)
If nothing else, both ends still share a common ground reference, yeah?
-You are right; I just looked it up. I guess (not that it makes much of a difference!) I picked this up from a book on earlier days of submarine cables.