Short answers, pulled from the story.
The Khazar Khaganate emerged as a new political entity in the year 630 from the ruins of the First Turkic Khaganate. A properly constituted state formed around 670 following the conquest of the lower Volga region and the subjugation of the Onoghur-Bulghar union.
The capital city of the Khazars was named Atil, which featured a dual-city structure with Kharazān on the western bank for the king and Itil proper to the East inhabited by diverse religious groups. This location supported a self-sufficient Saltovo economy combining pastoralism, agriculture, and fishing stocks from the Volga River.
Khazar royalty and nobility appear to have converted to Judaism sometime between 740 and 920 CE to deflect pressures from Arab and Byzantine forces. King Bulan is said to have convened a royal debate and decided to adopt Rabbinic Judaism after being convinced of its superiority during a journey to desert mountains of Warsān.
Arab forces advanced on the Khazar capital Balanjar in 652 but were defeated suffering heavy losses according to Persian historians such as al-Tabari. Warfare continued through the 720s with invasions into Armenia and Azerbaijan until conflicts ceased for more than two decades after 737 due to internal instability among Umayyads.
Nine skeletons dating to the 7th through 9th centuries excavated from elite burial mounds in modern Rostov region show mixed genetic origins including both European and East Asian paternal haplogroups. Samples do not show genetic connection to Ashkenazi Jews nor do results support the hypothesis that Ashkenazi Jews are descendants of Khazars.