When you install the PoodLL filter and the PoodLL Anywhere plugin for either Atto or TInyMCE, you must manually go add poodll to the Atto and TinyMCE Toolbar config setting areas. Go to Administration > Site administration > Plugins > Text editors > Atto HTML editor > Atto toolbar settings. In the included picture, you can see I have added a whole new poodll section with the Anywhere tools, the Generico filter, the Snippet plugin, and the Preview plugin grouped there.
I missed it in your original post, the file picker is disabled in those places where uploading a file is not permitted. To make it possible, you would have to re-write core code in those places.