Short answers, pulled from the story.
Brigadier General Borivoje Mirković was the primary organiser of the Yugoslav coup d'état, though General Dušan Simović served as the formal commander and became prime minister afterward. Major Živan Knežević and his brother Radoje Knežević were also central to the planning and execution. The dispute over who deserves primary credit was never fully resolved.
The coup was triggered by the Cvetković government signing the Vienna Protocol on the 25th of March 1941, binding Yugoslavia to the Tripartite Pact and aligning the country with the Axis powers. Officers in the Royal Yugoslav Air Force, encouraged by the British Special Operations Executive, had been planning the overthrow for months and acted within two days of the signing.
Prince Paul relinquished power the evening of the 27th of March 1941 and left with his family for Greece, then travelled to Kenya and eventually into exile in South Africa. He was convicted of war crimes in September 1945 for signing the Tripartite Pact, but a Serbian High Court officially rehabilitated him in 2011, ruling the conviction was politically motivated.
Hitler postponed Operation Barbarossa by approximately four weeks from its original date of the 15th of May 1941 on the same day as the coup. Whether that delay was decisive to the outcome of the Soviet campaign is disputed: in 1972 Martin van Creveld dismissed the causal link, while in 2013 historians Craig Stockings and Eleanor Hancock concluded there is "little doubt" the Yugoslav invasion forced some delay to the Soviet start date.
King Peter II was 17 years old when the coup occurred and was declared of age by the military conspirators without his prior knowledge. He heard the announcement of his own coming of age for the first time on the radio. He was inaugurated on the 28th of March 1941 in the presence of Serbian Orthodox Patriarch Gavrilo V.
The British Special Operations Executive encouraged and supported the coup plotters. British air attaché Group Captain A. H. H. McDonald met with Simović on the 26th of March, and intelligence agent T. G. Mappleback met with Mirković the same day, telling him the coup had to be carried out within 48 hours. Historian Marta Iaremko, writing in 2014, concluded that "the vast majority of researchers" consider the putsch was planned with British intelligence assistance, though British agency alone was not sufficient to ensure it happened.