Wiseman,

>>Does the CuteEditor support some sort of custom-events (javascript) like a "onStylechange"?

No.

>>Purpose of asking is that I want to make custom buttons for styles that are outside of the editor

itself, but needs to be updated with the current style in the editor.

In the following example, when you click the radio button, the Editor.EditorWysiwygModeCss property is changed dynamically.
 

 

So I suggest you create server side custom button to achieve what you want. There is an example showing how to create a server side button.

 

 

Hope it helps.

 

Let me know if you have any further questions.