Short answers, pulled from the story.
Burmah Oil created the Anglo-Persian Oil Company as a subsidiary on the 14th of April 1909. William Knox D'Arcy originally negotiated the oil concession with Mozaffar al-Din Shah Qajar in 1901 to prospect for oil across most of Persia.
The agreement granted D'Arcy exclusive rights to prospect for oil for sixty years across most of Persia. In exchange, the Shah received £20,000 and a promise of 16% of future profits while D'Arcy financed the venture with capital from his shares in the Mount Morgan Mine.
Reynolds struck oil shortly after receiving orders to cease work on the 26th of May 1908. This discovery came after Burmah Oil had sunk more than £500,000 into their Persian venture and decided to abandon exploration by early May 1908.
Iranian support for nationalization became intense by May 1951 due to grievances regarding the small fraction of revenues Iran received compared to company profits. APOC reported after-tax profits of £40 million in 1947 while the agreement entitled Iran to just £7 million or 17.5% of profits.
The anti-Mossadegh plan was orchestrated by the CIA under Operation Ajax and by SIS as Operation Boot. General Fazlollah Zahedi led tanks to Mosaddegh's residence and arrested him for treason before he was sentenced three years' solitary confinement on the 21st of December 1953.