Projects and Libraries confusion

IntelliJ IDEA 11.1.1:

Some puzzles with Projects, Modules and Libraries.

(1) From the Docs Basic Concepts > Project Structure I thought I understood that a Project was a way to manage, in coordinated manner, a number of individual Modules, where each Module could produce its own output (eg: jar).  Yet when I create a Project it has settings that look like it is a module in its own right, including having an src folder. This seems a bit confusing.  Is the idea here that one can choose to use either the Project-level src folderto build a single output, or ignore the Project's src folder and create multiple Modules with their own src folders etc?  Or is there some scenario where you would use both the Project-level src folder and some subsidiary Modules, with outputs from both the Project level and the individual Modules?

(2) I expected to be able to set various settings at the Project level, and have those be inherited by child modules. So if I set an external Library for the Project, I expected it to be associated with the child modules as well.  But that doesn't seem to work -- it seems to be necessary to add external libraries to modules individually.

Am I missing something here? Are project settings *not* inherited by child modules?  If that's the case, what is the advantage of a Project?

(3) Given the issue just described, in "Project Structure" dialog, Project Settings > Libraries, is there a way to view or edit which modules each library applies to?

(4) How do I add sources for libraries?  I looked all over the Project Structure dialog, and right-clicked everything, but couldn't find a way to add sources. (I did stumble on the Attach Sources dialog via a hyperlink that appears in the editor for files that lack sources, but that seems the long way to get there, no?)

Thanks,

-- Graham