Hi Peter,
we have attempted to reproduce the issue you have reported, but we could not find the path that leads to creation of documents in the global scope. (We could see that they were created in the schema you have sent us, but we need to realize how does it happen). The other issues you mention are most likely the consequences of this main problem.
Our support will contact you for further details and work with you on finding the issue that causes the Document to land in global part.
best regards,
Bratislav