Instead of moving the generated output file, just move the ibedmx file to the non-SL project of your choice. If you do this manually you'll also have to manually edit the relative path information (the path to the EDMX file) stored in the ibedmx. An easier way of doing this is by using the Object Mapper to target the projects you want: it will allow you to choose both the Silverlight and non-Silverlight target projects, or create new projects. When using the Object Mapper, it will also automatically link the generated designer.cs file in the Silverlight target project, and ensure that the namespace and assembly names are in sync. It's really not a good idea to move the designer.cs file on your own, since both the Object Mapper and the BuildWatcher (code which runs during builds) are specifically looking for the ibedmx file.
Re the probing error - the domain model (the generated designer.cs file) must reside in both a non-Silverlight project (a class library or the web project) and a Silverlight project (an SL class library or the Silverlight application), and is automatically added as a linked file in the SL project by the Object Mapper. In the Prism Explorer, you see the generated model in the ModelExplorer.ModelDF project, and the linked code in the ModelExplorer.ModelDF.SL project. Note that these class libraries both use an assembly name of ModelExplorer.Model. Take a look at the app.config in the PrismExplorer.Shell project, and the web.config in the PrismExplorerWeb project, for correct setup of the <probeAssemblyNames>.
We have a number of simpler, non-Prism, examples in the Learning Resources folder installed with the product. The "Four Simple Steps" tutorial is a good place to start.