Remove the game listing without removing the game

Yes, what you want to do is possible. While all 3DS software is region-locked, Nintendo DS software is not. Because that region-locking isn't encoded into the DS software, you can play software from all regions on your 3DS.

You can even check out this youtube video where someone demonstrates a DS games from North America, Japan, and Europe on their North American 3DS.

You are correct. Nintendo gave us folders and named ones at that with the capacity for up to 60 items and at the same time also gave devs the ability to push updates. Apparently nobody put up any official info about how to create folders yet so I'll just describe my experience in doing so (note that wherever I tap an icon/folder in the home screen, you can usually do the same by navigating to it with the D-pad and pressing A):

I haven't played my 3ds much lately, let alone update firmware although I did an update about 18 hours ago for the heck of it and folders weren't there yet. Upon reading your question, I:

Ensured the 3DS has the Latest Firmware Update:

1. powered on my 3DS,
2. double-tapped on System Settings (you can alternatively tap Open),
3. tapped Other Settings,
4. tapped the right arrow three times,
5. tapped System Update,
6. tapped OK in the lower-right,
7. tapped I Accept in the lower-right,
8. waited until it was done its thing and tapped OK to restarting.

I went through updating a second time, but it said I was up to date.

Then I figured out

How to Create a Folder:

As aro19 and Krazer suggested, to create a folder, you must:

1. tap an empty slot on the home screen (The SD card icon may look like an empty slot, but it isn't),
2. tap Create Folder on the bottom of the screen.

and there was a new folder. I did this again as I wrote this to document the process. The folders created will be named # (New Folder) which will increment and apparently deleting a folder will not reallocate the number for folder auto-naming (likely until it reaches the cap and then loops around).

You cannot create a folder within a folder.

Now that I had multiple empty folders I tried out folder management.

How to Use Folders:

Like the rest of the home screen icon management, it's pretty simple:

1. Drag an icon onto a folder to add it to the folder.
2. Tap a selected folder to view its contents or use Open in the lower-left.
3. Drag icons within the folder content window to swap their positions.
4. Drag an icon out of the folder content window and onto a space on the home screen to remove it from the folder.
5. Tap the right and left arrows or use the D-pad navigation to change screens to the left or right just as you would on the home screen.
6. The size of icons can be changed just as they would be in the home screen by using the buttons in the top-left corner of the screen.
7. Tap the curved arrow on the folder content window to close the folder content window.

How to Rename a Folder:

Folders will display the first character of their name as their icon.

1. On the home screen, tap the folder you want to rename,
2. tap Settings in the lower-left,
3. tap Rename on the upper half of the menu,
4. enter a new name on the text input screen,
5. and tap OK on the lower-right to accept the new name.

How to Delete a Folder:

Folders containing anything cannot be deleted.

1. On the home screen, tap the folder you want to rid yourself of,
2. tap Settings in the lower-left,
3. tap Delete on the lower half of the menu,
4. and tap OK on the lower-right and your folder will be gone.