Short answers, pulled from the story.
The Latin translations of the 12th century were a large-scale effort by European scholars to translate scientific, philosophical, and religious texts from Arabic and Greek into Latin. Scholars traveled to recently reconquered cities in Spain and Sicily, where Arabic-speaking populations and large collections of manuscripts gave them access to knowledge that had been absent from western Europe for centuries.
Gerard of Cremona, born around 1114, traveled to Toledo because he could not find Ptolemy's Almagest anywhere in the Latin world. After arriving and finding an abundance of Arabic books on every subject, he learned Arabic in order to translate them. He went on to translate 87 books, including the Almagest, major works of Aristotle, and Euclid's Elements of Geometry.
The Toledo School of Translators, known in Spanish as the Escuela de Traductores de Toledo, was the translation center that grew out of the Cathedral of Toledo following its reconquest by Christian forces in 1085. Raymond of Toledo led a team of Mozarabic Toledans, Jewish scholars, Madrasa teachers, and Cluny monks who translated works from Arabic into Castilian and then into Latin. Historians note it was more a practical bilingual environment than a formal academy, with only one translation definitively linked to Archbishop Raymond by name.
The first Latin translation of the Qur'an was produced in 1142 under the sponsorship of Peter the Venerable, the abbot of Cluny. He commissioned Robert of Ketton, Herman of Carinthia, Peter of Poitiers, and a Muslim known only as "Mohammed" to produce the work, titled Lex Mahumet pseudoprophete.
William of Moerbeke undertook new translations of Aristotle at the assumed request of Thomas Aquinas because the Latin copies then in circulation had passed through Arabic-to-Latin translation chains originating in Spain. Those translations were suspected of carrying philosophical and theological errors introduced by the rationalist commentator Averroes. Moerbeke translated directly from Greek to bypass that influence, and his translations were considered standard classics by the 14th century.
Sicily had been part of the Byzantine Empire until 878, under Muslim control until 1060, and then under Norman rule from 1060-1090. The Norman Kingdom of Sicily maintained a trilingual bureaucracy and ties with the Greek East, making it ideal for translation. Sicilians generally translated directly from Greek into Latin rather than from Arabic, and produced translations including Ptolemy's Almagest, works by Euclid, and Aristotle's Meteorologica Book 4.