You should never undertake any file management outside of the Organizer. The easiest way to move files that are already in your catalog is to click and drag them into the new folder location, using the Folders panel. Make sure you are in the Tree View of the Folders panel as this will make it easier to identify the folders than if you are in the List View.
We need more information to be able to diagnose why you can't see the files that you have imported into the new catalog. How did you "recreate" the catalog? Where are the "copied" files located on your hard drive, both before and after you copied them? You can do a search for a "copied" file in the catalog by pressing Shift+Ctrl+K and typing the file name into the text box that appears. If the file shows up in the search results, select the thumbnail and right click on it. You will then have the choice to Go to Folder. This will take you to the folder in the Folders panel where Elements thinks your file is located.
You can't use the organizer just like you are working in the Windows explorer without understanding the purpose of working with a catalog. In particular the 'drag and drop' interface metaphor does not have the same meaning.
For you, 'drag and drop' means copying files from one folder to another. That is something you can do from the organizer in several ways since most of what you can do in the Explorer is available in the organizer, the organizer sending orders to the Explorer routines to get the same effect. However the whole huge advantage of the organizer is to manage your media files from a powerful database storing links to the real location of the files in your computer. The catalog does not store any file, it works on links.
The first idea to manage your files on your computer is to use the Explorer commands to navigate in your folders trees. When you need to use a file for different purposes, it looks natural to copy the files in different folders depending on your purpose. Then you are creating unnecessary duplicates which should be absolutely avoided in any optimized and logical structure. The database is able to use the same file in different contexts without duplicating it. No risk to update or delete a copy leaving the originals unchanged for instance.
So, if you use keywords or albums structures, no need to duplicate your files.
The organizer, like other database assets manager, is built to help you prevent duplicates, that's what you have discovered by yourself. With the available keywords and albums structures in the catalog, you don't care much for the location of the files on your computer. It's easy and fast to perform complex multicriteria searches and even to reshape your logical keywords/albums structure when you want. A simple date based structure on your Explorer is good enough.
When you see the advantage of using the tools the organizer can offer, you also can find by yourself that even managing voluntary copies or duplicates is possible if needed.
First, the drag and drop metaphor is too imprecise to descrive which action the software has to do.
Realizing that a 'copy' command is what you really want to do will help you find the 'Copy or move to removable disk' command. It also works to copy or move to internal drives...
More logical would be to use the command 'file >> duplicate' followed by a file >> move to another folder. The move can be performed by dragging a file to another folder in the left folders panel in tree mode. There, the dragging metaphor is perfectly clear.
Very often, what you want to do may be achieved by a 'File >> export as new files' command with many options (format, size, renaming...) By default, the exported files are not included in the catalog, which does not create duplicates in the catalog.
I hope this may help you start understanding if and how you should use the organizer catalogs.