Brainstorming...

What could be good for Roman, greek, eastern, and 'barbarian' cultures...

The first thing that came to mind for the homeland resource was a large wooden door... -abstract, I know. Something administrative and shared... A Table with a map (similar to the one in the faction summary window, but not the same)... A Scroll or set of scrolls.... hmmm. Tough.

As for the "conquered: That is even harder because a greek type 2 isn't a colony or sword conquered territory. It is an athens style democracy, right?