With respect to (1), I can't offer much input except to say that perhaps there's an odd use case where somebody uses the system in a single-ended configuration where this makes sense.
For (2) my intuition is that you should just select one channel and stick with it. The nature of the common-mode noise is that it will be fairly uniform across the body, as the noise you're interested in is largely a manifestation of the impedance of the body connection to the reference electrode. Once the noise is on the body, the 300mOsm fluid all over the body is a pretty good conduction system.
I think there's also an argument to be made in terms of failure modes. If each 'trode has a certain percentage chance of having a failed attachment, your chances of corrupting the CM signal with a failed electrode is the sum of the the probabilities across channels.
Lastly, the good thing about choices like this is that changing a value to one or two registers can undo the choice in moments!