How to open and explore the codes of the system Palettes files

You can Get the palette, then apply MakeExpression in order to convert boxes into the corresponding high-level expression, and then display the result as InputForm. For example:

palette = Get@
   FileNameJoin[{$InstallationDirectory, "SystemFiles", "FrontEnd", 
     "Palettes", "SlideShow.nb"}];
InputForm @@ MakeExpression[palette, StandardForm]

If you aren't satisfied with the default formatting produced by InputForm, I recommend reading this answer of mine.