If I open the 'folders' icon on the lower panel there is no 'File System' shown  ... Can it be added?

If it's the Directory Menu Plugin you're mentioning the you can choose which folder it represents (right-click>Properties).

You can add a custom action for that with either Catfish itself or other GUI like gnome-search-tool, if you prefer a GUI.
If you mean just search something in the Thunar window all you need to do is to start typing the name of what you want and Thunar will focus that.

Is there any way to add search capability to Thunar or is Catfish the only way to go? It's a nice search tool but I would like a quick access from Thunar.

David