Short answers, pulled from the story.
The British Parliament passed the Statute of Westminster 1931 on the 11th of December 1931. This law fundamentally altered the nature of the British Empire by transforming it from a hierarchy of rulers and subjects into a voluntary association of equals.
The main effect of the Statute of Westminster 1931 was the removal of the ability of the British Parliament to legislate for the Dominions. The statute declared that no British law could extend to a Dominion unless that Dominion explicitly requested and consented to it.
The whole statute applied to the Dominion of Canada, the Irish Free State, and the Union of South Africa without the need for any acts of ratification. These three countries gave their consent to the application of the law to their respective jurisdictions.
Australia adopted sections 2 to 6 of the Statute of Westminster 1931 with the Statute of Westminster Adoption Act 1942. The adoption was backdated to the 3rd of September 1939, the date that Britain and Australia joined the war.
The Irish Free State never formally adopted the Statute of Westminster 1931 because its Executive Council believed the Anglo-Irish Treaty of 1921 had already ended Westminster's right to legislate for the Irish Free State. Éamon de Valera used the abdication of King Edward VIII to remove all explicit mention of the monarch from the Constitution of the Irish Free State in 1936.
Newfoundland never adopted the Statute of Westminster 1931 due to financial troubles and corruption, leading the United Kingdom to establish the Commission of Government in 1934. That arrangement remained until Newfoundland became a province of Canada in 1949 following referendums on the issue in 1948.