2. All concrete classes that extend PageMediator and that implement IPageMediator do not seem to need to contain any of the methods that are declared on IPageMediator and I can add as many public methods as I want even if they aren't declared in IPageMediator.
Adrian addressed both issues well, but the thing about #2 that you might still be missing is that the framework facade method retrieveMediator returns an IMediator. You're looking for a more specific interface (IPageMediator), so you have to cast if you want to access those methods:
Assuming there could be multiple page mediators registered:
var pageMediator:IPageMediator = facade.retrieveMediator(pageMediatorName) as IPageMediator;
-=Cliff>