Short answers, pulled from the story.
The International School, developed in England and regulated by the World Dance Council and WDSF, uses Standard and Latin categories each containing five dances, for a total of ten. The American School, regulated by USA Dance, uses Smooth and Rhythm categories for a total of nine dances, and permits open and separated dance positions that the International School does not allow.
The ten International competition dances are divided into Standard and Latin categories of five each. Standard covers Waltz, Tango, Viennese Waltz, Slow Foxtrot, and Quickstep. Latin covers Samba, Cha Cha, Rumba, Paso Doble, and Jive.
The Viennese waltz is recognized as the oldest of all current ballroom dances. It originated in the Provence area of France in 1559 and was introduced in England as German waltz in 1812.
Mambo was developed in the late 1930s by Orestes López and his brother Cachao, of Arcaño y sus Maravillas, as an offshoot of danzón, the national dance of Cuba. In the 1940s, Dámaso Pérez Prado adapted it for big band and brought it to Mexico and the United States.
Judges assess dancers on criteria including poise, hold or frame, posture, musicality, timing, body alignment, floor craft, and presentation. In finals, officials called scrutineers apply the Skating system, assigning each couple ordinal placements typically from 1 to 6, after tallying recalls accumulated across rounds.
The Blackpool Dance Festival, held annually at Blackpool, England, is considered the most prestigious event a dancesport competitor can attend. It includes events for both individual competitive dancing and formation dance.