How can we download the workbench from the FME server showing the output of each transformer in the downloaded workbench? I want to get the joins and unjoins from the databasejoiner transformer.

If your FME Server user account allows for downloading workspaces you can do so from Workbench, there's a "Download from FME Server" option in the file menu, as well as on the toolbar. You'll need to supply your credentials or already have a web connection to that FME Server set up. Workbench will then download the workspace.

You'll need access to the source data as well of course, but if you have you can run the workspace locally and use Feature Caching to inspect intermediate results.