As for rendering, sort of. I would call it compositing only, since the compositor does nothing at the surface level (except for the composite surface, that is). It instead copies the visible contents and performs any math needed for any enabled special effects. Actual rendering (as in taking the input of the app and turning it into an image) is client dependent, and will most likely be done with toolkits and OpenGL.
As for window management and toolkits, the only part they perform should be window decoration.
As for input, I think it's handled by Wayland (the protocol, not any of its compositors) and the compositor chooses who gets the focus.