Using Time Machine with an Airport Extreme AirDisk
P1. "The Backup disk image could not be created."
If you get this message when
backing-up to a network drive, check your Computer Name at the top of the System Preferences > Sharing panel.
It must not be blank; it should not be more than 25 characters long; and you should avoid punctuation and special characters (even though OSX may use some when it makes the default name when you first set up a Mac).
After changing it, if the LocalHostname didn't change automatically, click the Edit button and make the corresponding change to it.
Apply the same rules to 
the name of your Airport Extreme via Airport Utility:
Note: if you're using Airport Utility 5.6.x, click your Airport in the sidebar and click Manual Setup at the bottom. You'll find similar windows.
Apply the same rules to 
the name of your Network via Airport Utility:
Time Machine can back up to a USB drive 
connected to the new, tall Airport Extreme "ac" models (6th generation) introduced in June, 2013.
But it's not reliable and not supported by Apple on the older, flat models. They have different hardware. If there's trouble with it, you won't get much, if any, help from Apple. If you decide to take the risk, you'd be well advised to have other backups; don't depend on these 100%. See Time Machine FAQ #2 for supported Time Machine destinations.