1) when using the Editing Online option for this board in Carafe Kitchen v3.1.3, I see several files that are editable. The most useful apparently is “template.carafe” where I can change font colors, board title colors, and probably add some additional classes to the existing 3. Is there any additional files worth editing and why?
2) I presume that since the actual Kanban javascript code is not being stored locally, along with Bootstrap, that there is not a way to edit any of those files, and that none of the API function shown on the GitHub page for this library is available? Or if I am misguided how would I go about doing this?

3) I have successfully added additional parameters to the $data json block (responsivePercentage, dragBoards, etc) but cannot seem to get addItemButton and buttonContent to work. Some sample code would be wonderful?

Take a look at "Anatomy of the Carafe Bundle" in the tutorials. 

 

This tutorial was made before we added "libraries" to the bundle format, but it still covers the fundamentals, and it shows demos of working with a bundle in Code Sandbox.

To answer your question about modifying the library code, you are correct, you would not want to directly edit libraries.

Since you're working in Code Sandbox, you could post your sandbox here with the issue(s) you're having.