When you add the Apple ID as the iMessage account details does it indicate it is not registering ?
Try putting the iPhone in Airplane mode for few minutes and restart Messages app on the Mac once the iPhone in connected again.
This creates a Start Point" as it seems the expected set up is Mac first, iOS device second (and third).
When you restart Messages it should get an alert from the iMessages server that the iPhone is using the iPhone Number and Apple ID.
Repeat for the iPad is required.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously