Short answers, pulled from the story.
The assassination of Caliph Uthman occurred in 656 CE and created the First Fitna, which split the Muslim community into three distinct paths: the Sunnis, the Shias, and the Kharijites.
The four Sunni schools of jurisprudence emerged in the 8th century CE and were founded by Abu Hanifa al-Nu'man for the Hanafi school, Malik ibn Anas for the Maliki school, Muhammad ibn Idris al-Shafi'i for the Shafi'i school, and Ahmad ibn Hanbal for the Hanbali school.
Shias comprise 10 to 13 percent of the global Muslim population and believe that leadership is a divine right reserved for the Prophet's family, specifically Ali ibn Abi Talib and twelve specific successors known as Imams.
The Qadiri order was established by Abdul-Qadir Gilani in the 11th century and the Mevlevi order was founded in the 13th century, with the latter emphasizing dance and music as a path to divine love.
The Ibadis are the only surviving branch of the Kharijites and today form the majority of Muslims in Oman and significant minorities in North Africa.
The Ahmadiyya Movement was founded in 1889 by Mirza Ghulam Ahmad in British India and its followers are branded as non-Muslims in countries like Pakistan because they claim Ahmad was the promised Messiah and a subordinate prophet.