I have no direct experience with the 503cw body, however in the CFVII 50c Instruction Manual (downloadable from Hasselblad), it is listed in section
1.10 Connectivity Chart - Mechanical Shutters as being the same as the 500C/M body in the
Cable Free Operation panel. In other words, just fit the back to the camera, power the back on, set the ISO and other specifics on the back (such as crop, preview behavior, etc), then set focus/exposure with the body and lens, make your photos. It works seamlessly with the 500C/M this way; I can only presume that it works the same with the 503cw. When you want to use it in Live View mode, you set the back to work in that mode with electronic shutter specifically.
According to the same chart, the 503cw is also compatible for use with Phocus Remote Control operation when used with the Winder CW motor drive. This requires the exposure cable connection be used. The 500C/M is not compatible with Phocus in this way.
With all Hasselblad V system bodies (and V system back compatible alternative cameras), you can operate them via the CVFII 50c back's controls as a "shutterless lens" using the electronic shutter and Live View capabilities of the back. As with the 500C/M, just lock the camera with the back and lens shutters open and the lens stopped down, do the rest of the operation using the back's controls.
I also have no experience with Phase One digital backs. You should probably ask that question in a thread where people using those backs with Hasselblad 500 series bodies are conversing, or start a new thread pointed specifically at that topic.
It should be obvious, but for completeness: The 907x body is incompatible with Hasseblad film backs. It lacks the mechanisms to wind those backs' film transport, the shutter, and/or trigger the shutters with anything other than the CFVII 50c back.
G