An auxilliary bishop may or may not succeed a diocesan bishop. It is entirely up to the Holy Father. Often, auxilliaries move to a diocesan vacancy in another diocese after some experience assisting a diocesan.
However, a co-adjutor bishop is appointed specifically to succeed the diocesan he is assisting, and will do so immediately, without further action necessary, when the post becomes vacant through death or resignation (or technically removal, too). We have a co-adjutor Archbishop here in Vancouver, Archbishop Miller, who was appointed (from a Vatican curial post) to assist Archbishop Roussin. He will, in the normal course of events, succeed him.
Unless he is a co-adjutor, a bishop has no claim to, and cannot be assumed to be in line for, succession.
As for the prayers in the canon of the Mass, that’s a variable. In the US, the General Instructions for the Roman Missal do not appear to allow for more than one bishop (the diocesan) to be named, with others being merely referred to. (We pray for N., our Bishop, and his assistant bishop(s).) In Canada, it seems to be up to the diocesan. In our Archdiocese, Archbishop Roussin has directed that the prayer be offerred for “our Bishops Raymond and Michael.”
Now as for the Anglicans, same old, same old. Nothing to see here, folks. Might as well just move along. Disintegration and degeneration is a horrible thing to watch anyway.
