Does every jurisprudential school of thought have its own unique usul al-fiqh (principles of jurisprudence), and is the science of usul al-fiqh divided into four types, corresponding to the number of jurisprudential schools?

Every jurisprudential school of thought has its principles, and there are agreed-upon principles. Works on Usul al-Fiqh (principles of Islamic jurisprudence) can be categorized based on several considerations: according to the schools of thought (Hanafi, Maliki, Shafi'i, Hanbali, Zahiri), and according to the method of writing: the method of the Mutakallimun (based on rational evidence), the method of the Fuqaha (linking rules to branches), the method combining both, and the method of deriving branches from principles. A beginner is advised to study a concise work on Usul al-Fiqh under a proficient شيخ (scholar), such as "Al-Waraqat" by Al-Juwayni or "Tayseer Ilm Usul al-Fiqh" by Al-Judai'.