About the wyrd sisters
Unlike wizards, witches don't vie for ranks in hierarchies, don't like to live in the same huge building, and don't gather except for a potluck during a necessary meeting to discuss boundaries. These are boundaries not of power but of duty, for a witch is generally the midwife, doctor, life adviser, and moral policeman of a village.
Your average witch is not, by nature, a social animal as far as other witches are concerned. There's a conflict of dominant personalities. There's a group of ringleaders without a ring. There's a basic unwritten rule of witchcraft which is 'Don't do what you will, do what I say'. The natural size of a coven is one. Witches only get together when they can't avoid it.
Works with your device
Headology works like psychology, but many witches think "psychology" is a bad word, or that it means "having a psychological problem". The practice of headology relies on the principle that what people believe is what is real (for that person).
The broomstick is the device for magically enhanced travel favoured by witches.
While associated with witches, wizards have been known to use them in extremis.
Up to Date
The edge between life and death, light and dark, good and evil, today and tomorrow, this world and the next... and many others. An "edge witch" watches over and guards these edges. Edge witches learn to think fast, because edges can shift so quickly. It also hones senses that most people never know they have.
Consider a witch's cottage as the permanent free hospital in a village, where the word "free" is used loosely in this context. Money may not change hands, but respect is a sort of social currency, and a debt of responsibility to take care of one's witch is also at least implied without being specified.
Formula Incantatricarum et Catalogus Praecantricarum, or Matrix Sagarum
Being a Directory of All the Witches of the Discworld ... of whatever manner or Tradition, be they Great or humble, as
record is made of him/her/zir/hir/xem/them in any Book.
Salé Gadula! ...Miché Gabula! ...Bibi Te! ...Bobi Te! ...Bu!