Short answers, pulled from the story.
Thoinot-Arbeau published the book called Orchésographie in 1588. The text detailed movements like the basse danse and the branle performed in large rooms designed for such gatherings.
Louis XIV founded the Académie Royale de Musique et de Danse a decade after 1650. This institution formulated the five positions of the feet that would influence ballet technique for over two centuries.
The waltz emerged as a country folk dance in Austria and Bavaria during the 17th century. It entered England around 1812 and faced initial opposition due to its closed hold before eventually softening societal resistance.
The Standard category includes International Waltz, International Tango, International Viennese Waltz, International Slow Foxtrot, and International Quickstep. These five dances form part of the ten dances required for a Ten Dance competition under World Dance Council regulations.
Harry Fox named the foxtrot in 1914 after he rapidly trotted steps to ragtime music. Partners face one another while frames rotate from side to side changing direction after each measure.
Enrique Jorrín developed Cha Cha in the early 1950s as a slower alternative to Mambo originally called Triple Mambo. The dance features many hip rotations with partners synchronizing movements while bending and straightening knees.