How to move files to a new sub directory

When you use the file>export command, the files are not imported automatically to the Organizer catalog.  So, you will need to import them into the catalog separately.  It is possible that the files will not be imported into the catalog if you use the same format for the export as the Organizer will treat the files as unwanted duplicates.  I gave you this option because I thought that you only wanted the files to use for outside service providers or to show on your TV (and did not want duplicates).  If you change the name or the format of the files, you may be able to import them into the catalog, if that is what you want to do.

An .xmp file is what is known as a sidecar file.  It contains all the information about edits that have been made to the original raw file which never changes.  This allows non-destructive parametric editing of the raw file.  All edits to the file such as exposure and color are stored as digital numeric values in the .xmp file which is a simple text file.  If you delete the .xmp file, all edits will be lost but the original raw file will remain.

Hmmmm . . . . Yes, there can be issues with stacks.  Here is another suggestion.

But first, yes, you should edit the raw files before converting them to jpeg.  You will get much better results IMO and the raw editor is much easier to use and more powerful than editing jpegs in the PSE Editor.  For sending many photos to sharing sites, you may also want to try the Organizer's Instant Fix editor.  I just used it to send about 40 raw files to FB.  The Auto Fix command within the Editor does a great job of fixing exposure and white balance issues with multiple files in batch mode and easily saves and converts the raw files to jpeg.  It also seems to improve noise quite nicely.  The other tools within the Instant Fix editor are also very good, particularly the Clarity tool.

Here is another strategy, whichever editor you use:

• In the Organizer, select all the files you want to move to a new folder.  It doesn't matter whether they are stacked or unstacked.  If you want to move the raw files only (and they are on top of the stack), simply select the visibile files.
• Choose File>Export as New File(s) . . .   This will open a new dialog.
• Browse to the folder where the new files will be stored.  You can create a new folder within the dialog.
• If you want to convert the raw files to jpegs for sending to your service provider, you can do that here.  
• Only the selected files will be exported to the new folder.

Hope these suggestions fit your needs.

It's not clear from your post how you are moving the files.  If you are doing so in Windows File Explorer, stop!  All file management must take place in the Organizer.  Otherwise, you will end up with missing files in the catalog. 

Here is what is required:

First, make sure that your My Folders panel is in Tree View.  Click on the down arrow at the top of the panel and make sure View as Tree is checked.  (See screenshot below.)

Next follow these procedures:

1. Right-click on the folder with the raw files you want to move;
2. Select New Folder from the context menu.  A new folder will be created and you can specify a name. However, once you create the new folder, it will probably disappear from view (because the default is to display only folders with files that have been imported into the catalog).
3. Right-click again on the parent folder containing the raw file.
4. Select Show All Sub-Folders from the context menu. 
5. The new sub-folder will now be displayed.
6. Select all the raw photos you want to move, and click and drag one to the new sub-folder.

Now, I have to ask you why you want to isolate the raw files.  There may be other methods to accomplish your goals.  The Organizer is simply a database and it doesn't care where the files are stored.  If you only want to see your raw files in the grid, you can simply do a search for file names, using the raw file's extension.  There are several other possibilities.