The problem I'm encountering is that the base objects are not being copied when I mass select, copy the area and paste it into the other cell.
You probably don't mean base objects, right? Base objects are defined in the Object Window. Everything placed in a cell is a reference to one of those. At least I think, ha! Wondering if you mean something that I don't understand when you say base object.
To do what you're describing I always right-click on the cell's name in cell list (left window) and choose duplicate. The CK creates a pretty exact copy... all you have to do is rename the new cell. If there were a few things that you didn't want, find them in the object list (right window) and remove them there.
I'm not sure, but I'm willing to bet the reason some things don't copy when you do a select all in the object list is dependencies. That is, you have a decal applied to a certain wall. When the CK goes to copy that decal, the wall it paints on may not have been copied yet, so it has no where to go. Copying the whole cell usually gets around this.
It sounds like you might have tried that already. Not sure what would stop an NPC from being copied. Did you check to see if it has the "Unique" property flagged? I don't think the CK checks but it might.
I suppose it could be dependencies again. Does the cell you're coping from use other mods or assets that aren't available? The CK might show you place holders but the copy could skip anything it can't find. Go to File -> Data... and select the file that contains the source cell. Hit Details and scan that list for anything that looks suspect.