Regarding the Succession of Witches
In the noble families of witches, family secrets are often inherited by a single child to prevent a propagation of hidden arts and a subsequent decline in their quality.
This rule applies for the Endless witches, so their most secret arts are passed down to a single pupil, and once one has passed down these arts to another, they retire to further stem their propagation.
Custom dictates that a witch from another sect make a recommendation before a succession may occur.
Lambdadelta recommended EVA Beatrice. Bernkastel recommended Ange Ushiromiya. It is unknown who recommended Beato.
Furthermore, during the story, Beatrice inherited that name along with the position, but that is a very recent innovation. The Predecessor was the original Beatrice, and all Endless Witches before her had different names. After that, it became customary for the name to be inherited as well, and EVA Beatrice followed that tradition when giving ANGE the name of Beatrice.
Beatrice's Titles (golden and endless) are passed down through different unrelated means. The former involves solving The Portrait Epitaph while the latter is a long
During the coronation of Evato, Beatrice confirms she is inheriting both titles.
According to Maria's diary the main criterion for coronating a golden witch seems to be solving the epitaph.
But unless we completely write off the tips as magical nonsense, we know the sequence of endless witches is recommendation based and it pre-dates Virgilia by some generations, hinting at a different real world parallel.