Is a human, an exceptional one but a human.
The not ageing thing might be a technology issue. The Eleventh Doctor might have done something like this because in "The Impossible Astronaut" the Doctor has 907, and then he is 1103, and that would be 196 years (without ageing), but in Trenzalore he lives there for 300 years (and ageing a lot).
But the thing is that the origin of The Church of the Papal Mainframe is human (there where some Anglicans in the Church, also the structure of the Church is the same as in Catholicism, but with all the military things).
And the thing about the Dalek-conversion, might be the same as when Craig stopped the Ciber-conversion process, with willpower and, let's say "love".