King Mohammed Zahir Shah (1914-2007) came to power in 1933 following the assassination of his father.  For most of his reign, the real power lay with his two uncles, Sardar Mohammad Hashim Khan (Prime Minister 1929-1946) and Sardar Shah Mahmud Khan (Prime Minister 1946-1953).

In 1973, the King was in Italy undergoing eye surgery when Daoud Khan staged a coup d'etat.  He abdicated and remained in exile in Italy for 29 years.  After the 2001 invasion, the US opposed his reinstatement, and instead he was given the ceremonial title "Father of the Nation".  He moved back into the Kabul palace and died there after a long illness.

A cleft lip/palate, or "harelip", results from incomplete fusion of facial elements during gestation and occur in 1 in 700 births.  Modern western medicine can correct the deformity with straightforward surgery, although treatment may need to continue throughout the growth phase of the child.

Kite-fighting is a popular sport in a number of Asian countries, including China, Korea, India and Thailand.  In Afghanistan, it is known as Gudiparan Bazi.  Competitors attempt to snag each other's kites and cut their strings.  To this end, kite strings are smeared with a mixture of glue and ground glass.  Kite flyers may bind their fingers to protect them against the abrasive strings.

 

           

 

Under Taliban rule, kite-fighting was banned in Afghanistan. 

For the British Empire, Afghanistan was considered a serious threat to their "jewel in the crown", India.  Britain feared invasion by the Afghans, or by Russians through Afghanistan during the era of strategic rivalry known as "The Great Game".  Consequently, Britain attempted to gain control of Afghanistan over a period of decades, fighting three Anglo-Afghan wars.

The first war (1839-1842) resulted in the destruction of the British Army during its devastating winter retreat from Kabul.  Only one Briton escaped.  The second war (1878-1880) was a British victory, and resulted in Britain gaining control over Afghan foreign affairs, an important advantage in the struggle with Russia. 

The third war (1919) began with an Afghan invasion of British India, a serious challenge for British defenders so soon after the Great War and the Amritsar Massacre.  It lasted just a few months and resulted in the British repelling the invasion but losing their control of Afghan foreign affairs.  Consequently, Afghans celebrate their "Independence Day" on 19 August, the day Britain signed the Treaty of Rawalpindi establishing the furthest boundary of the Empire at the Khyber Pass.

It is not clear what this game is.  One analyst reckons Hosseini is describing a Russian game, Prostoy Durak.  Otherwise, Internet references all point to The Kite Runner.