Yes, it is possible to have both DxDesigner 2005 and 2007 working. We suggest having 2 different wdir paths because some files are different in each environment. Use the configurator to switch between releases.
On your second question, the last version of IO designer to support Dx2005 was 2007.3 Please refer to our support net technote MG243984.
I have more details on running Dx2005 and Dx2007
I have Dx2005 installed at C:\MentorGraphics\exp2005
Dx2007 is installed at C:\MentorGraphics\2007.6EE and 2007.8EE
Run configurator -clean to switch between versions and then run the configurator with the appropriate versions to correctly install the registry entries and start icons.
The 2007 configurator is located in this directory C:\MentorGraphics\win32
The 2005 configurator is located here in my install: C:\MentorGraphics\2005EXP\win32