Something that interests me from a linguistic/neurological point of view: Do Chinese native speakers actually thinkg about the parts of compound words that have a completely different meaning from just the sum of the compounds when using them? Like 东西 ("East-West"), or 西红柿 ("Western red persimmon")? Or are they just like standalone words on their own?
When I saw a tomato first in my life time, I was told its name was fanqie(番茄) by my mom or dad in the dialect. I was not able to recognize or write any character then. All I knew about the tomato was that it was a red, green, or yellow, and delicious vegetable and sounded fan qie. I thought it was another kind of 茄子(eggplant).
Later, after I went to school and learned to speak Putonghua and write characters, I got to know that fan qie is written as 番茄 and it has another name 西红柿. As my teacher explained, 番 refers to foreign. 番茄 is a kind of eggplant-like thing from a foreign land. The name makes sense. So does 西红柿, western land's red persimmon. But now when it comes to 西红柿 or 番茄, I don't think about what each character means. It's just a name of an object.
In some cases, I may not really care about each character's meaning from the very beginning. For example, 深圳. It's a city of Guangdong province. If 圳 alone is seen, I may not recognize it at all. Seldom can I see it elsewhere. It's always part of 深圳. So I don't know its meaning till now without referring to a dictionary, and I'm sure it won't take long before I totally forget it even if I look it up.
Another example is a transliterated word like 咖啡. I didn't figure out what 咖 or 啡 means until I learned the English word coffee. And all of a sudden, I got to know there are many such words in Chinese, like 坦克(tank), 沙发(sofa). A single character in such word has no specific meaning but just indicates the pronunciation. Of course there are some translated words that concern about both the meaning and pronounciation like 迷你(mini), 可口可乐(Coco Cola), 露华浓(Revlon) and etc, some of which are really beautiful and elegant master pieces of translation.
A third example is a word like 麒麟, kirin. I thought it was just a creature in myth, and didn't try to find out what 麒 or 麟 means until I watched an anime， the Twelve Kingdoms, in which there are kirins that can transform to humans. The female kirins are named X麟 and the male X麒, where X is a character that has similar pronounciation with the name of the kingdom the kirin belongs to. After some research I leaned that 麒 refers to a male kirin and 麟 a female kirin. So does 凤凰, phoenix, 凤 as male and 凰 as female. But in the word 龙凤, 凤 represents a girl or woman.
There are some characters in my dialect I have been expecting to find out how to write. Some have been clear, but the others have not. There is a dirty character that means the f word. It sounded exactly the same with 十(ten) in the dialect. Since it's a dirty word, I just didn't dare and felt embarrassed to ask my parents or teachers how to write it correctly. My little fellows and I just wrote it as 十. In the circumstances, we all knew it meant the f word. About one year ago, I happened to read someone's post and get to know the right character should be 入(go into, penetrate). A 20-year-old question was finally made clear. However some of the unclear may stay mysterious till my last day.
I believe every character in a compound word makes sense, indicating either the meaning or the pronounciation or both. Now I always tend to find out what each character means when I see a new word . And I would do the same to the old words, expecting to find some interesting stories. It helps to get a deeper understanding and also bring benefits especially when learning ancient Chinese.
I am a Chinese native speaker, and I personally view words like "东西" as an entity, rather than "东"+"西".
From my point of view, all Chinese native speakers would simply judge such words as standalone words. In fact, all characters are meaningless until they are grouped to words.
On the other hand, I suppose, say, English native speakers won't identify "nevertheless" as "never"+"the"+"less", either.
As a native Chinese speaker, I learn the words directly and don't try to think about how it came about the first time.
Let's start viewing it from the character scope rather than the word scope. Children usually learn some complicated character, e.g. 聽 ("listen", 听 in traditional Chinese), by decomposing them into reasonable or unreasonable fragments of the character, e.g.
耳王十四一心, i.e. easy-to-read mnemonics to help memorizing. But that's only for writing the words. A native writer would be too familiar with it and doesn't even look at these parts. This is like learning the word "breakfast" in English -- some people learn it by remembering "break fast", but you don't think about it anymore if you are familiar with that word.
On the other hand, if you stare at the characters for a long time, they may decompose into fragments in your eyes and you would doubt if you wrote the word wrongly. For example, the character 的 (preposition for possessive relationship, or less used as the center of an archery target) combines 白 (write) and 勺 (spoon), which does not have apparent relationship with the word.
This is similar to the case you mentioned, except that this is within the same character, while you are talking about compound words, which have a more apparent spacing between two words.
東西 is a very common word, so a mature native speaker almost never remembers that it means "East West".
This is like the phrase "touch wood" in English. I don't know about the etymology of this phrase, but I'm sure that many people say it without being aware of the material "wood", but merely as an unconscious saying (especially when what they're about to say after "touch wood" usually makes people uncomfortable). I think this is comparable to how it is used in Chinese.
The special feature in modern Chinese is that most content words are in duplets. I think this phenomenon is like how children say "Mommy" rather than "Mom" -- as if one extra syllable (yes, one character in Chinese should be considered as one syllable rather than one word) makes the word more meaningful.
Therefore, when reading long sentences, just like we (at least I do) format an English sentence into subject+verb+object structure in English, one would first group characters into words, and then word phrases, and then parts of speech, and then the whole picture of the sentence.
A fact to note is that while every Chinese character has its own meaning, in compound words, closely related with the meaning of the characters (such as 跑 "run" 步 "steps" as in 跑步 "run"), or not (such as 東 "east" 西 "west" as in 東西 "thing"), few people would notice the individual meanings. So when grouping characters, 跑步 should be thought as one word rather than a verb+object phrase.
Of course, there are also instances where sometimes words are thought as one or two words, especially when it comes to modern technology stuff. The word 伺服器 (server) is made up of 伺服 (serve) and 器 (machine). I'm not talking about 伺服, where both characters are related to the meaning of "serve". "Server" obviously has a distinctive meaning than "serving machine" (sounds like an auto teller machine or a waiter robot). Therefore, people who know what a server is would view all three characters as one word, but people who don't know what a server is would understand it as a "serving machine", so it becomes two words. This is just like people who don't know what a smartphone is know that it is a phone that is smart, and people who know what a smartphone is have a totally different approach to understand this word.
Classical Chinese scope
This is a little off-topic, but this is also partially related to your question, depending on whether your definition of "native speakers" also includes ancient people.
In classical Chinese, texts are much more simplified due to scarcity of resources in ancient China and time-consuming of copying, especially before paper and movable characters printing technology were invented. Therefore, often, one character stands for its independent meaning, unlike how it is in modern Chinese. For example, 妻 (wife) 子 (son) means "wife and children" in classical Chinese, but 子 is used only as a suffix like the
my as in
mommy, so only 妻 is meaningful in modern Chinese, so 妻子 is one word standing for "wife" in modern Chinese. However, there are many instances of 妻子 standing for "wife and children" in ancient texts (and thus one of the reasons why classical Chinese might be more difficult to read for native speakers).
I beg to differ. Regardless of language, speakers sometimes reflect on the composition of words and their etymology. This is probably more true in languages that strive to keep their uniqueness, like Chinese and Icelandic, rather than languages that are littered with loan words.
Chinese speakers are able to see the logic behind words like 危机, but do not understand imports such as 经济 or 沙发 in terms of components.