Short answers, pulled from the story.
Sharia is the immutable, infallible law of God revealed in the Quran and Sunnah, while Fiqh is the fallible, changeable human effort to comprehend that divine will. Fiqh serves as the dynamic style of research and practice that expands Sharia through the interpretation of the Quran and Sunnah by Islamic jurists known as ulama.
The golden age of classical Islamic jurisprudence spanned from the early second century AH until the mid-fourth century AH. This era saw the emergence of the eight most significant schools of Sunni and Shi'i jurisprudence before the fall of Baghdad in 1258 CE marked the beginning of a dark age.
Muhammad ibn Idris ash-Shafi'i codified the basic principles of Islamic jurisprudence in his book ar-Risalah between 767 and 820. He proposed that priority be given to the Quran and Hadith before looking at consensus or analogical reasoning.
The Hanafi school is prevalent in Turkey, the Balkans, the Levant, Central Asia, South Asia, China, and parts of Egypt. It is also the basis for law in Saudi Arabia and Qatar alongside the Hanbali school.
Islamic jurisprudence influenced Western law through institutions like the Hawala value transfer system and the Waqf trust system which developed between the 7th and 9th centuries. These concepts influenced the development of agency in common law, civil laws such as the aval in French law, and the English trust law that emerged during the 12th and 13th centuries.