The problem you are having is likely related to the Room Bounds, which are used to optimize large cells in-game. The NV-GECK has a problem rendering objects in a Room Bound even inside the GECK, so you have to work around this.
If your just starting out, my recommendation would be simply to delete the portals and room bounds in your Duplicated cell (never do this in a vanilla/Obsidian-created cell).:
1. Load-up your duplicated interior cell in the "Cell View" window (obvious step but I want to be thorough).
2. Click on the "EditorID" column heading on the Right Side (not the Left side showing all the interior cells) in the Cell View, which will sort the list of references in your duplicated cell alphabetically.
3. Find the "RoomMarker" objects, there should be a list of a dozen or so. Select and delete these room bounds.
4. Press F5 to re-render the cell, after which you should see everything.
Normally such a radical step is neither necessary Nor recommended as these room bounds can optimize cells for players. Without them, it means the entire cell must render when the player enters your bunker (wether they are in a room or not). For most PC players this wont mean much at all unless you have a HUGE cell, which the Brotherhood of Cells cells are not. For your first-time playing around with a cell however, it will be much easier to not have to worry about the Room Bounds given the NV-GECK issue.
With the room bounds removed you can GECK your new cell as much as you want to. Later on when you get more familiar with level design, I recommend following Bethesda's YouTube tutorial on Optimization. That tutorial will teach you how to Add room bounds and portals, so you can add them back to your own cell later on when your done as a learning exercise.
Luck,
Miax