I'm really interested in how culturally unified and how diverse ancient China was. In the anglophone world we seem to look at China as a monolithic culture, but I know that it's an extremely diverse country even today. I want to know how it was in the past.
The "warring states" were all considered Chinese, I lnow, but how unifying was that at the time? China is an exremely diverse country, built on expansion throughout its history - absorbing, assimilating, and being influenced by the cultures it encountered. How thoroughly were conquered people incorporated into China? Could they achieve high status or were they just subjects? Were they already closely culturally linked or were they seen as totally different?
I kind of get the impression that it was like imperial Rome, where it was ethnically diverse, but also had a strong unifying force in the imperial government and its institutions. By the late Roman Empire, the distinction between "true" Romans and Romanized Thracians, Illyrians, Gauls, etc. seems really blurry. Is this similar to how Chinese culture came to be seen as so unified?
First off, yes, it is important to remember that China is far from monolithic today. Linguistically, culturally, in cuisine etc it has a diversity comparable to Europe and in many ways is best conceived of as a continent in and of itself. This was also very much true in the past.
That being said, the Spring and Autumn and Warring States period did see a cohering of what we think of as "Chinese" culture across most of what we think of as the Chinese heartland. This heartland did not include all of what we now think of as "Chinese" China--most notably, Sichuan and south China remained outside of Chinese control until the later Warring States period and Han Dynasty, respectively. Within the area of "China", however, a very strong sense of common culture and common identity developed. Chu, which was centered along the Yangtze, is often portrayed as Other and only semi-Chinese, but archaeology has largely not borne this out and it seems the alien depiction was a later literary trope. This isn't to say all the areas of China were exactly the same, but their variation is coherent within a larger Chinese cultural unity.
That being said, there is always the question of to what degree this is merely a reflection of a common elite culture. And of course, a lot of variation in internal meaning is likely being missed. The study of "Sinification" is unfortunately still somewhat in its infancy and the neccesary archaeological research has often not been done. In fifteen years it might be possible to give a much better answer to this.
Good sources dealing with this are Flad and Chen's Ancient Central China, Yang's between Wind and Cloud, and the recent Cambridge volume China's Early Empires: A Re-appraisal.
This is a great question, but it's not one that we really know the answer to. Firstly, I think your comparison with Rome is fairly accurate - the Zhou Dynasty that preceded the Warring States period seems to have provided some common cultural references points and a written language for all of the Warring States, much as Latin and Roman culture diffused across Europe.
As to how different people were, it's extremely difficult to say because of the minuscule amount of primary documentary evidence we have of the period - most of our knowledge of the Warring States era comes from texts (such as the Zuo Zhuan and the Shiji) that were compiled in the Han Dynasty, hundreds of years after the fact. Moreover, the Han ruled over the former Warring States and claimed descent from the Zhou Dynasty, and as such for official historians (who provide our only records from the era) to emphasise any ethnic or cultural divisions among its subjects might have been politically dangerous. For these reasons, the Warring States tend to seem more homogenous than they probably were.
That said, quite a bit is known about the state of Chu (located south of the Yangtze) from the historical texts and from poetry attributed to Qu Yuan, a Chu native. The Chu appear to have spoken a non-Chinese language that was probably related to modern Vietnamese, and appear to have had a distinct shamanistic religion that may have involved human sacrifices. I wish I could tell you more but beyond that, not much is known.