Short answers, pulled from the story.
The Commonwealth of Nations is an international association of 56 member states, the vast majority of which are former territories of the British Empire. In 2023, its combined population was 2.5 billion people, making it one of the largest voluntary associations in the world.
The Commonwealth was created as the British Commonwealth of Nations through the Balfour Declaration at the 1926 Imperial Conference and formalised by the Statute of Westminster in 1931. The London Declaration of April 1949 is regarded as the beginning of the modern Commonwealth; it allowed India to remain a member as a republic, dropping the requirement to recognise the British monarch as head of state.
Charles III is the Head of the Commonwealth. The position is not hereditary; when the monarch dies, the successor to the crown does not automatically become the new head. Commonwealth leaders agreed in April 2018 that Prince Charles should succeed his mother Elizabeth II, establishing a precedent rather than a rule.
Mozambique, a former Portuguese colony, became the first country admitted without any constitutional link to the British Empire when it joined in 1995. Rwanda, a former Belgian and German territory, joined in 2009. In 2022, the former French territories of Togo and Gabon also joined the Commonwealth.
Members can be suspended "from the Councils of the Commonwealth" for serious or persistent violations of the Harare Declaration, particularly failures of democratic governance; suspensions are decided by the Commonwealth Ministerial Action Group. No country has ever been formally expelled, though South Africa's reapplication in 1961 was effectively blocked due to opposition to apartheid, and Zimbabwe was suspended in 2002 before withdrawing in 2003.
The Commonwealth Games are a multi-sport event held every four years, started in 1930 in Hamilton, Canada, as the Empire Games. They include standard athletic disciplines alongside sports particularly associated with the Commonwealth, such as netball, squash, and lawn bowls. The 2022 Games were held in Birmingham and the 2026 Games are scheduled for Glasgow.