>>Is this the correct configuration? (A one word answer will suffice)
No.
You don't need a bin directory for each web directory.
Your configuration should be as following:
c:\intepub\wwwroot\CuteEditorClientFiles
c:\intepub\wwwroot\bin\
If c:\inetpub\wwwroot\MycoolWebSite is a sub-directory of your web root, it's enough.
If c:\inetpub\wwwroot\MycoolWebSite is a virtual directory, you can use the editor.FilesPath property to spefiy the path to the editor client files.
Editor.FilesPath Property
asp.net Chat http://cutesoft.net/ASP.NET+Chat/default.aspx
Web Messenger: http://cutesoft.net/Web-Messenger/default.aspx
asp.net wysiwyg editor: http://cutesoft.net/ASP.NET+WYSIWYG+Editor/default.aspx
asp wysiwyg html editor: http://cutesoft.net/ASP
asp.net Image Gallery: http://cutesoft.net/ASP.NET+Image+Gallery/default.aspx
Live Support: http://cutesoft.net/live-support/default.aspx