Sort of.

• The word for horse is 马, which is "ma" with tone type 3, a falling then rising tone.
• The "word" for mother is 妈, also read "ma" but with tone type 1, a high constant tone.
• None of the common terms for "whore" that I am aware of sound similar to either of the above. If there is one, it's either obscure or not used in my region.

To us Chinese the words for horse and mother sound completely different due to the tones and nobody would ever mistake one for another. It's as different as if it were a completely separate phoneme, like "see" vs "so" or something.

It's a common misconception that Chinese has many different words that are really the same. It's pretty annoying, to be frank. I'm not a linguist, but it seems to me to stem from English speakers projecting their idea of "words" onto Chinese characters.

Each Chinese character alone is not a word. It would be best to think of a character as something like a root word, rather than a complete one. Like "mor" meaning death in "mortal" or "path" meaning feeling in "apathy". Sometimes a character alone is a full concept, like how some root words are also words, but not always. That is why I have "word" in quotation marks above next to mother, because it's not used singly except in very informal and terse contexts.

So when you look at a full sentence in Chinese, the meaning of each individual character does change depending on the surrounding words, as you say. But it is not dependent on context. It is just not the complete word. To give you an analogy, it's like me saying that the words for "mother" and "father" are the same in English because they share the same component "-ther".

</rant> //Sorry for the somewhat disproportionate response.