Ah yes, the Circular Quay question.
My understanding is that within the internal computer systems for signalling and train control and so on, each run of a diagram can only become the next run of that diagram (or "change run number", to use s3_gunzel
's terminology) at one point. For the City Circle, this changeover point is Circular Quay. (The same used to apply to Birrong/Regents Park for Bankstown loop trains, where Birrong/Regents Park was the changeover point.)
Now, from the customer information perspective, a City Circle train has a different start and end of the run. Let us take an example of an up South Line train forming a down Airport Line train, by going around the City Outer (i.e. first stop Town Hall). Going by passenger information displays and printed passenger information material, the South Line run terminates at Museum while the Airport Line train commences at Town Hall. From the passenger information perspective, it is therefore two runs at once; this is something the computer systems cannot handle, because they can only see one train on one run (at a time).
So within the computer systems, the up South Line run terminates at Circular Quay and forms the down Airport Line train, i.e. the train terminates at Circular Quay; hence, the onboard passenger information displays change over at Circular Quay.
For the record, I believe this is also why the older Grant Goldman digital voice announcements (as still used at Olympic Park) state that trains to the City Circle terminate at Circular Quay (e.g. Central, Town Hall, Wynyard, Circular Quay.
should be more than familiar with this.