If you are going to use organizer, you must use organizer. Do not move photos in the finder or the organizer will not know what you did with them. If it annoys you to have to use your photo manager to manage your photos, don't use organizer.
While the new organizer is somewhat more folder friendly than previous versions, the whole point of a program like organizer (or iphoto) is to stop thinking about the physical location of your images and manage them with tags and albums instead.
I'm not sure what you mean by
I also experience folders in Elements Organizer that should not exist.
One example: Directly in Finder, I created a new folder and moved pictures from two folders which I then deleted. In Elements Organizer, I still see the old structure (no new folder - still the deleted folders included the picture files).
Not sure if you have used the 'My Folders' or 'Show folder list' in the left folder panel ? Those two ways to display and work with folders must be understood before doing experiments, especially if you use Finder/Explorer to control results. You need to give more details on your procedure to make things clear.
See the video about the 'New UI' in the welcome screen.
And of course, Barbara is right about giving the priority to managing media files by tags albums and dedicated organizer tools.
Thank you for your helpful answers. I have been using other organizer tools before, and they were structured differently. As allways - starting with a new system, you jump right into it instead of reading the instructions carefully. I now have the full picture after proving and failing. Also the FAQ mentioned above explaines it in an easy way.
The best way to make changes to files or folders, are to do it inside Elements Organizer. If you do changes outside, i.e. Finder in mac (which I did), afterwards you have to reconnect to the right files.