You can either export all NPC's (for example) by ticking the NPC box or individual ones by dragging them into the export window. You cannot export a group of NPCs.
If you are simply editing an existing module all of the edits that you make will be stored in a file which has the same name as the module that you are running in the moduledb folder inside the campaign that you modified it. So, for example, if you were running Curse of Strahd then inside the campaign folder for the first group of players you'll find a folder called moduldb and inside that you'll find a file called D&D Curse of Strahd.xml. You can copy this file from one campaign into the same folder in another campaign and it will have all of your edits in it and when you open the Curse of Strahd module in that other campaign the moduledb file will over-ride the official module.
However this file will not contain anything that you have added yourself - such as a new image or an item or NPC that you have created from scratch rather than just edited from an existing item or NPC. For those items you will need to export them. Since these are things that you have created wholly within the campaign you can just click on the NPC or item tick box and only those items will be exported.
What you can't do is export your edits if you simply edit an existing entry in a published module. (This will be why you are seeing stuff get 'lost in transit').
You can also have a third campaign where you do all of your creating (again by this I mean not editing an existing module but adding things such as items, NPCs, images etc) and export those things into a module which can then be opened in any campaign you like.
Be sure that you are backing up all of your campaigns regularly because when you start doing this kind of thing it is very easy to get confused or mixed up and end up with a mess.
