Displacement controls in the Surface Layer are indeed not equivalent to a Power Fractal. If you want controls that are available in a Power Fractal, use that, or you can plug the output of the Power Fractal into the Displacement Function input of a Surface Layer if you just want the displacement from it. For multiple children, you stack them, one leading into the input of the next (nested children), keeping in mind that they will influence each other's coverage. It's easier to visualize with the Node List on the left in the Shaders layout.
I suspect you're misunderstanding the purpose of the Parts shader (as well as the multi shader). Both are for object UV mapping only, and shouldn't really be used outside of the context of imported objects. Parts shaders are created automatically when you import an object with associated UV maps. Because of the need to be associated with existing UV maps, they can't be created manually at this time.
Perhaps it would be easier to give specific advice on an approach if you start from a base explanation of what you're trying to achieve. It sounds like you want to mix multiple surface shaders? This can be achieved in a couple ways, depending on how you want them to mix and what shaders you're using. It's not that frequent that entirely separate shader networks need to be merged, but if you do need to do that (particularly if based on some mask), try a Merge Shader.
- Oshyan