Short answers, pulled from the story.
The meaning of the name Kipchak varies by source, with some traditions claiming it translates to hollow tree while other scholars suggest it means angry or quick-tempered in Siberian dialects. Peter Golden proposes a better match involving words for good fortune combined with an adjectival suffix.
The Mongols defeated the Alans after convincing the Kipchaks to desert them through pointing at shared language and culture. Köten led forty thousand families into Hungary where King Bela IV granted refuge in return for Christianization before they were forced to flee again after his murder.
A late thirteenth-century dictionary known as the Codex Cumanicus preserves words in Kipchak, Cuman, and Latin. This document stands as the most important surviving record of their language alongside Turkic-speaking Mamluk dictionaries compiled in Egypt.
A genetic study published in Nature on the 2nd of May 2018 examined remains of two males buried between one thousand AD and twelve hundred AD showing increased East Asian ancestry. One male carried paternal haplogroup C2 and maternal haplogroup F1b1b while another displayed pronounced European ancestry with maternal haplogroup D4.
Al-Mansur Qalawun served as Mamluk sultan of Egypt ruling from twelve-seventy-nine to twelve-ninety and Baibars was another Mamluk sultan reigning from twelve-sixty to twelve-seventy-seven with Kipchak ancestry. These leaders were part of a group where many Kipchaks became mercenaries or slave warriors after their defeat by Mongols.