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. Another possibility is that this functionality might be important for lead-off detection, or the plethysmogragphy mode for respiration detection. It's a fairly beefy chip, with a variety of bells and whistles, and one of the bells and whistles you're not using might explain the need for this functionality.
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!