PART I

So this is an interesting question, and answering it is going to be complex. A big part of why is because, frankly, our sources are limited - most of Kazakh traditional culture was oral, and we don't get very solid sources until well after the formation of the Kazakh Khanate in the mid-15th century. We start getting written histories and studies by Russian observers in the mid 18th century, and only start getting written versions of Kazakh law codes, oral histories, and epic poems in the 19th century. Perhaps there are some earlier records, but they would be written in an Arabic script, would have been of limited interest to the largely illiterate population, and would be largely outside the knowledge or abilities of any subsequent Russian-language sociological or historic studies anyway. As an aside V.V. Vostrov and M.S. Mukanov are the big Soviet-era names in researching clan and tribal history of the Kazakhs, so a lot of Kazakh ethnography is heavily indebted to them.

As for Zheti-ata, or “seven grandfathers”, the primary importance of this particular custom seems to be in terms of determining familial relations. Kazakh society was strictly exogamous, and so anyone sharing a common ancestor back to seven generations was considered a cousin and ineligible for marriage - conversely, anyone sharing a common ancestor would be considered family and deserving of particular support from extended family members, should they need it. While auls (villages) tended to be groups of extended families, they weren't necessarily organized per se along the lines of all members sharing a common ancestor seven generations back.

As far as hordes (zhuz) and the clan (ru), these are probably a bit more significant in the period before Russian conquest, as they were essentially the organizing units for a Kazakh identity. While Kazakhs had traditions of the three hordes coming from Alash and his three sons, the idea of a common Kazakh ancestry is something of an invented tradition, as it seems that the three hordes coalesced in the 15th and 16th centuries on a geographic basis, and were composed of tribes that had disparate origins. In the case of the Middle Horde, we are talking about peoples living in modern-day northern and central Kazakhstan, and belonging to six ru: Argyn, Kerei, Naiman, Qipchak, Qongirat, and Uaq. Kerei are supposed to have Mongol origins, while other ru such as the Qipchaq are supposed to have a Turkic origin on the Western Steppes. There are also Uzbeks who belong to the Qongirat and Qipchaq ru, so these clannic identities don't map neatly onto modern ethnic identities.

It's also worth pointing out that ru were divided into sublineages, so these themselves were not necessarily the building blocks of Kazakh governance. Kazakh society in the pre-conquest period mostly saw village and clan elders the (aksakal) appointing a bii or judge, who would provide some level of justice and order in relations with khans and their sultans, who tended to be Chingisid descendants and made up something of an aristocracy of “white bones” (ak-suiuk). Of course Russian conquest in the 18th and 19th centuries began to break down these structures, and Soviet collectivization largely completed that process.