1.) Mohammed was raised in Mecca by his uncle. At that time, the people there all worshipped over 300 different gods, most of which were just clay statues. Wealthy people ruled Mecca and so Mohammed went into a cave to try and think of a solution. Mohammad claimed Gabriel taught him the ways of Allah, the one true god. From Mohammed's dictations, his disciples wrote those teachings down and it became the Koran. Mohammed moved to Medina, where the Koran was developed. He was learning lessons from Mecca.
2.) There are five; the first is declaration of faith - To say and believe that there is no diety except God and the Prophet Muhammad is his final Messenger. The second is to pray 5 times a day, and then the third is to fast the Holy Month of Ramadan. The fourth is to give to the poor a percentage of your wealth, and lastly the fifth is Hajj - To make a pilgrimage to Mecca at least once in your life.
3.) The main problem was the succession. There was a disagreement by those who thought it should run in the Prophet's immediate family and those who did not.
4.) The Abbasids came to power during a rebellion in Persia. The chief leader of the rebellion was Abu al-abbbas, a descendant of Muhammad's uncle. During the 740s Abu al-abbas's party rejected Umayyad authority and seized control of Persia and Mesopotamia. Abu al-abbas then founded the Abbasid dynasty, which became the principle source of authority in the dar al-Islam. The Abbasid dynasty differed considerably from the Umayyad's one being the Arabs continued to play a large role in government, but Persians, Egyptians, Mesopotamians, and others also rose to positions of wealth and power, and the Abbasid dynasty differed from the Umayyad also in that it was not a conquering dynasty.
5.) People who followed Islam contributed very much to the development. The first cities were in the middle east, and the first Universities were in Islamic Countries, specifically Morocco. In general Islam encourages free thought, science and culture generally, as such many people that lived in Islamic areas helped those areas grow. Agricultural technology is developed on a necessary basis, so when cities grow, people find new ways to grow food. Industrial, not so much because the industrial revolution was really England and the US in the 18th and 19th Centuries, however the Islamic world was leaps and bounds ahead of the rest of the world in regards to technology.
6.) Arab conquerors spread the word of Islam,