Catherine, Holy Katherine question

Re-reading the NS, currently almost finished with Citadel.

SPOILERS

Severian's mother -and by extension Ouen's wife, is revealed to be Catherine, a former Pelerine who got convicted of something -perhaps adultery- and was given to the torturers. So we can assume that she gave birth before she died and the baby was raised as a torturer.

What's the connection between Catherine and Holy Katherine, the patroness of the guild? Is she a clone -if so, how come Severian as Autarch does not know anything about it since the person is so significant to him-? If she is a time-traveler does she use the Corridors like the Green Man or technological means, and whatever the means, why does she does so to die again and again every year?

Finally, is there any connection between this Catherine and the Catherine from the Talos's play?

Thank you.