Short answers, pulled from the story.
The name Cuman appears in ancient Roman texts as a designation for a fortress or gate before becoming a people. In Turkic languages qu, qun, qūn, quman or qoman means pale, sallow, cream coloured, pale yellow, or yellowish grey.
The Cumans first encountered the Rus' in 1055 when advancing toward the Pereyaslavl principality. A war started by chieftain Sokal in 1061 lasted 175 years involving repeated invasions and battles such as the Battle of the Alta River.
The Mongols crossed Caucasus mountains meeting Cumans in Subcaucasia in 1223 leading to defeat at the Kalka River battle. Large-scale westward migration began after conquest with the first wave appearing summer 1237 crossing Danube into Bulgaria.
King Béla IV offered refuge remainder of Cuman people under leader Khan Köten December 1240 hoping to use new subjects as auxiliary troops against Mongols. Barons assassinated Köten Pest March 17 which triggered a slaughtering vast number Hungarians leaving Balkans Second Bulgarian Empire going rampage destruction Hungary equal Europe experienced since incursions Mongols.
Cumans first seen Byzantine resources 1078 began serving mercenaries Byzantine army reign Emperor Alexios I Komnenos. In 1259 2000 Cuman light cavalry fought Nicaean Empire Battle Pelagonia majority 800 troops under Alexios Strategopoulos retook Constantinople 1261 were Cumans.