Guide to the Clans and Warriors of Kerensky have probably some of the most useful info.
How do you think the lower castes live?
In general not to dissimilar to the houses in most aspects. Though it differs between the clans and casts.
The lower castes use grades, how do you think the lifestyle would differ per grade?
Well their are 25 grades in the civilian casts, Grade 1 is very basic low wage stuff so you will not have much, pore food and a communal living space would not be to far off the mark. Grade 25 gives you better food, more "income", a larger living space (often your own home).
Medical care is very advanced, but also highly rationed to younger people over the older ones (and by your cast and grade).
Transit systems also are cast and grade based, while mass transit systems are available for all, a personnel vehicle is a symbol of higher "rank". Though it's rare for them to have one permanently assigned to them.
What do you think their architecture would look like? Civilian? Military?
Per WoK Your typical Clan city is rather drab and plain looking, cookie cutter layout, simple architecture. Though impotent government buildings are more impressive, The Hall of the Khans on Strana Mechty is built with a Gothic style. Also these buildings very between the clans, The Falcons and Wolves like Dynamic structures, where as the Jaguars like(ed) simplistic forms
What about art, music, theater, etc?
For visual arts cast need nought apply, A warrior is just as likely to be a painter as a member of the Merchant cast
Though their are some areas where your more likely to find some types than others. Performing arts are less prevent among warriors and scientists than the other casts -even then it's formed a sort of super cast (mostly from the laborer and merchant lines) to fulfill the needs. Though it's biased to the clans way of life. books are not all that common in the clans.
Would they dedicate someone to the task of making music for people to listen to, or would it be wasteful? Would one clan think it is wasteful vs another clan thinking it is not?
It would likely very from Clan to clan and from cast to cast.
On visual media (Trivid TV) Clans like the Jaguars have very little media outside essential broadcasts, so have little media industry, on the other hand the Diamond sharks have a huge industry that equals some IS powers in size and ability.
Clan "TV" is driven by needs rather than demand (as is for the most part the rest of their economy) So it provides mostly just information and indoctrination.
It's also cast based, Warriors are more military oriented, Historical battles, weapons tech, grate military leaders, scientists are well more about science and information. The other casts are a bit more like what we would know of, ranging from News (controlled), documentarys, Cooking shows and soap operas, again with a pro clan bias.
Theirs even Children shows one of the more popular is a series called Clan Spaniel, which features the exploits of of a group of anthropomorphic warriors in their fights to liberate their home worlds from the five tribes of evil monkeys (aka the IS houses), led by their parrot Khan "Polly".
Once again it's all about the clans...
Sports are common clan warriors, and possibly to a lesser extent other casts
Some of the most popular being Lacrosse and Football ("Soccer", American football and Rugby) -Clan Ghost bear is fond of the American football type, and in fact used this to it's advantage on the world of Sheliak when they played a game for control of the world -the Bears won 84 to 3 (it's very popular among Elementals you see).