Please check how are registered your original files path and names in your original project file.
Set them as relative to the original project (with resources in the same folder of course).
Copy your corresponding resources in the new project folder.
Then copy your layers from the original project to the target project.
It should be ok.
Surely about sound or image layer
That issue happens when you import a Synfig file into your new file.
I really don’t know if there is an easy solution for that, but in my projects I just use copy&paste between opens Synfig files… and it works enough fine for me. You can animate it without problems (it is just a new layer)
Of course, if you change the object pasted it don’t change in the original file… but it’s fast copy&paste again.