Short answers, pulled from the story.
The Kipchaks were Turkic nomads who most likely originated in the Altai region and were first unambiguously mentioned by Persian geographer Ibn Khordadbeh in his Book of Roads and Kingdoms. They expanded westward after the collapse of the Turkic Khaganate, joining the Kimek confederation and eventually forming a joint entity with the Cumans that stretched across the Pontic-Caspian steppe.
After the Mongol conquest of the 1230s, Kipchaks scattered in multiple directions. Khan Köten led 40,000 families into Hungary, while others integrated into the Mongol Golden Horde, and still others fled to Egypt where they founded the Mamluk Sultanate in 1250. Those who remained under the Golden Horde gradually blended Mongol and Kipchak Turkic identities into what became a Turco-Mongol culture.
The Codex Cumanicus is a late 13th-century dictionary compiling words in Kipchak, Cuman, and Latin, and it is the most important surviving written record of the Kipchak-Cuman language. It was produced because the Turkic-speaking Mamluk rulers of Egypt created a demand for Kipchak-Arabic grammars and dictionaries, which scholars still use today in the study of old Turkic languages.
The original Kipchaks practiced Tengrism. From 1120 onward, a Kipchak national Christian church existed after Georgian King David IV baptized large numbers of Kipchaks and married a daughter of Kipchak khan Otrok. Islam later became the official religion of the Golden Horde Kipchaks during the reign of Özbeg Khan, though it fused with older syncretic practices rather than replacing them outright.
The northwestern branch of the Turkic language family is called the Kipchak branch, and its descendants include Kazakh, Kyrgyz, Bashkir, Nogay, Volga Tatar, and Crimean Tatar speakers. Groups traditionally identified as Kipchak descendants include the Kumyks, Karachays, Balkars, Siberian Tatars, and Lipka Tatars, and Qypshaq remains a named tribe within the Middle Horde confederation of the Kazakh people.
The Mamluk Sultanate, founded in 1250, was established by the Bahri Mamluks, who were enslaved and refugee Kipchaks who had fled Mongol conquest. The state was sometimes called the "State of the Turks" because its ruling class identified with Kipchak Turkic heritage. Notable Kipchak-descended sultans included Baibars, who ruled from 1260 to 1277, and Al-Mansur Qalawun, who ruled from 1279 to 1290.