Ali Bin Abi Talib was murdered during the Fitnah (test/trial that touched the Muslims that started during Uthmans (May Allah be pleased with him) reign).
He was killed while praying by a non Muslim.
Ali
Yes.
The fourth Caliph was Ali ibn Abi Talib (Radi Allahu Anhu).
Muslims chose Ali in 656.
The question asks about the problems while he is caliph not before being elected as caliph. The first main problem was the opposition of some people to pay the ZAKAT as they were doing in time of the prophet. He waged war against them to oblige them to do as they were doing in time of prophet.Answerwhile he was Caliph Ali (sa) and more then 100 of Sahaba did not accept him as Caliph because they said Allah and prophet have selected Ali (sa) as Caliph at Ghadir. Ali (sa) neve willingly given Bayat to Abubakr. and also many Sahaba.
Caliph Ali was assassinated by Kharijites in 661 C.E., resulting in the end of the Rightly-Guided Caliphs.
There were a few events that he took advantage of to become the leader of the Islamic Caliphate. Firstly, he pressured Caliph 'Ali unreasonably about the assassination of his kinsman, the former Caliph 'Othman. Secondly, after declaring war on 'Ali, he managed to trick 'Ali into declaring that he was unfit to be Caliph which lost him the support of Khawarijites in Egypt. Finally, Mu'awiya defeated 'Ali's armies while (separately) a Khawarijite zealot assassinated him.
Hazrat Ali RAU was the last Rightly Guided Caliph. Hazrat Umar bin Abdul Aziz is also considered a Rightly Guided Caliph as he also rules justly.
Caliph Ali was assassinated by Kharijites in 661 C.E., resulting in the end of the Rightly-Guided Caliphs.
He is the fourth Caliph Ali Ibn Abou Taleb (Allah be pleased with him)
Al-Rashid - Abbasid Caliph - died in 1136.
Az-Zahir - Abbasid caliph - died in 1226.