Short answers, pulled from the story.
The Territory of Papua became independent as Papua New Guinea on the 15th of September 1975, during the Whitlam government in Australia. Australian Minister for External Territories Andrew Peacock had overseen the transition to self-government three years earlier, in 1972.
Queensland Premier Sir Thomas McIlwraith ordered police magistrate Henry Chester to claim the territory for the Crown in 1883, but Britain rejected the annexation. Britain then established a formal protectorate on the 6th of November 1884 and annexed it outright on the 4th of September 1888, naming it British New Guinea.
Hubert Murray served as lieutenant-governor of the Territory of Papua from his appointment following the 1906 royal commission until 1940. His appointment came in the aftermath of two successive commissions that recommended the removal of most senior territorial officials, including the administrator who had requested the second inquiry.
The Battle of Milne Bay took place in early September 1942, when Japanese marines attacked a Royal Australian Air Force base near the eastern tip of Papua. The Australian Army repelled the attack, making it the first outright defeat of Japanese land forces anywhere in the Pacific theater during World War II.
The delay stemmed from changes of government, elections, and a prolonged dispute over alcohol policy. Temperance advocates pushed for universal prohibition across the territory, blocking agreement until the Deakin government passed the Papua Act 1905 in November 1905 with a compromise: a local option for liquor licences combined with a ban on alcohol sales to Papuan natives.
The Territory of Papua was a Possession of the Crown, while the Territory of New Guinea held first a League of Nations mandate and then a United Nations trust territory designation. This distinction was maintained even after the two territories were merged administratively in 1949 and lasted until independence in 1975.