Chinese characters are NOT ideographs
Your first sentence is spot on. Unfortunately everything that follows is an old myth. Chinese characters are a single written form only in much the same way that the Latin alphabet is a single written form. They certainly don't guarantee mutual intelligibility in the languages that use them. A single character will have a certain pronunciation in any given Chinese language (and a different one in a different language – put (typically) two together and you have a composite symbol that represents a spoken word* not a concept or idea. As with any other language the written form is primarily a way of recording the spoken form – It's just Chinese just a lot more ad hoc in the way it does that recording.
*Or something like it. For example, 'kung fu' is accidentally two words in English because Chinese characters are written without any sort of word grouping, but it could just as easily have been transliterated as 'kungfu' and no one would be saying it wasn't a word. On second thought, t's probably better not to talk about words and just refer to the things that have dictionary entries whatever they are.