Short answers, pulled from the story.
A federation is a union of partially self-governing provinces, states, or regions under a federal government. The self-governing status of the component states and the division of power between them and the central government are constitutionally entrenched and cannot be altered by a unilateral decision without a constitutional amendment.
About 40% of the world population, or approximately 3.2 billion people, lives in a federation. There are 27 federations in the world, with 6 each in Africa, Asia, and Europe, 4 in North America, 3 in South America, and 2 in Oceania.
The United States is the oldest surviving federation, with its Constitution effective on the 4th of March 1789. The newest is Nepal, whose constitution went into effect on the 20th of September 2015.
A confederation is a permanent union of sovereign states for common action toward other states, while a federation's component states are not fully sovereign. A confederation has no real direct powers, takes day-to-day decisions by special majorities or unanimity rather than simple majority, and requires unanimity to change its founding treaty.
Switzerland is officially the Swiss Confederation, but the name is now a misnomer because the Swiss cantons lost their sovereign status in 1848. Despite the official name, the country functions as a federation.
Some federations are called asymmetric because certain states have more autonomy than others. Malaysia is an example, where Sarawak and Sabah agreed to join the federation on different terms and conditions from the states of Peninsular Malaysia.
A federation can collapse when its government cannot build institutions to mediate linguistic, ethnic, or religious differences, leading to secession or civil war as in the United States, Nigeria, and Switzerland. Collapsed federations include the Federation of Rhodesia and Nyasaland, the Gran Colombia, the United Provinces of Central America, and the West Indies Federation.