Specificly, I want to move three named references of the object XMarkerHeading from a location in "Tamriel" to a location in "WhiterunWorld". I don't want to mess up any scripts that use those references. Should I just delete them and create three new references of XMarkerHeading, with the same names as the old ones? Or would that create problems?

Whatever you do, don't *delete the references in the render window as "Deleted" references can cause stability issues (thus TES5Edit's UDR). If you need to remove stuff placed by official plugins, set PlayerREF (found in "(any)" cell from the dropdown box) as their enable parent and tick the "Set enable state to opposite of parent" flag(s) which will safely ensure said references are never rendered. You should be able to move those XMarkers with Ctrl+C/Ctrl+V from the render window and retain all of the reference info so long as the FormIDs stay as they are. With the same EditorID(s), yet different FormIDs, you'd end up potentially borking Skyrim reference info/quests/etc. as those XMarkers' FormIDs would be dead ends.

*nigh invariably, outright deletion of any official forms is bad practice.

Edit: Also, there's paste-in-place, but I forget the shortcut.

Specificly, I want to move C00AelaGiantHuntMARKER, C00AthisGiantHuntMARKER, C00RiaGiantHuntMARKER, and C00FarkasGiantHuntMARKER.

There are probably scripts that call on these names. How do I make sure those same scripts call on the new markers, instead of the old ones?