I tried to import a .DOC file into the binder.
I got: Could not convert file - Error: Unknown Error.
Same thing with DOCX but not with a PDF, which imported perfectly.
Do the same files import successfully into a Windows-based installation? If so, that points to something missing in your WINE environment.
Scrivener uses Aspose(a third party library) to convert DOC, DOCX and other file types to RTF, to import them in Scrivener. Most likely this library does not run smoothly under Wine. Try using other Wine apps to manually convert DOC to RTF and import the RTF file in Scrivener. PDFs are imported as they are and cannot be edited obviously.