You should be able to view a file even if it is checked out as long as it has been checked in at least one time.
Under the "Display" EPDM menu select "Options" and see if "Show bitmap for DWG-files" is checked. If it is not checked then you should be using eDrawings for the preview. You might try to do a repair on EPDM and see if that will get the viewer straightened out.
My recollection is that the Convert Task will not make PDF files from DWG files because it uses SolidWorks. If you have paid for DraftSight API, a program could be written to use it to make PDF files.
EPDM 2011 SP2
In a recent service pack (2011 SP3 I think?) they added the ability for the convert task to work with DWG files.