I see that you wrote this over 2 years ago, but a late answer is better than none. No, they don't have a character for every single word. That would be nearly impossible, because if you include names and technical words the average person knows tens of thousands of words. Chinese uses a lot of character combinations, reducing the number they have to memorize. I read a statistic saying that an average, educated Chinese person knows about 6000 characters. Still a whole lot!