What I would like to say is that I think the Warring States would fit the campaign mode for China at that time (they have different general leaders and units, but basically follow the Han structures), since apart from special units, leaders, etc., I don't think there would be many differences from the Han for a separate civ with new structures and units, though of course I could be wrong.
The Kushan Empire was a separate entity, more closely linked to India, and was essentially considered the leading power in Central and South Asia during its peak.
I don't quite understand what you mean, but yes, Qin Shi Huang unified China. Basically, the states mentioned were the strongest among the many vassal states of the Zhou dynasty. Essentially, the Zhou dynasty was a unified dynasty with supreme power in China, but the nobles were granted titles and land, forming their own territories, which later became vassal states. Nominally, they were loyal to the Zhou king, but gradually, central power weakened, and the vassal states grew stronger and conquered each other – that was the Warring States period. The names above are five of the seven most powerful vassal states.