And I think that none of the changes in the "common" diagram/instances are inherited to the child diagram/instances. Am I doing something wrong?
No, it's just like that. The instances in one package have nothing to do with the instances in another one. Looks like this is not what you need after all.
As to the version control approach:
Since the several projects are saved in the same repository (database). I would be able to import the elements from the "common" diagram, but won't I have the same problems then?
No separation into "Common" and "New" needed there. You just take the old model, put the package under version control, and then from outside EA with a version control client (like TortoiseSVN) you copy the xmi file(s) to a branch. Then you create a new empty model (eap file), configure it to point to the branch as local working copy for version controlled packages, and import the xmi file(s) via the "Get Package" menu. Then change the model as needed.
The problem there is merging back, but it should be possible with baselines. Anyway though, you wouldn't have what you call "inheritance" there, so I guess it's not what you want either.
So let's try another approach (again with the minimal example of A calling B in the old model and A calling C in the new one):
In package "Common", define A and B with a flow from A to B. Then in package "New", create a second Activity named A, and a new one called C, and a flow from the new A to C. Drag A from "Common" to the diagram in "New" where the new A and C are. Draw a dependency from new A to old A, perhaps giving it a stereotype like "overrides".
This way you don't change package "Common", and can now make the new A composite to model its details.