time machine backup to external HD via AirPort Extreme

is there any advantage to Secure Shared Device via Account or Device Password?

Accounts will not work if you are trying to back up using Time Machine since the account will not show up as a destination for backups.

Device Password....which is the default setting for the AirPort Extreme..... tells the AirPort Extreme to use the same password as the Base Station for the hard drive.

There is an option to use a separate Disk Password if you don't want to use the same password for both the Base Station and the Disk.

Did you partition the drives via the Disk Utility in the Mac?

Did you use GUID partitions? This may not be absolutely required but it is a good idea.

Did you use standard Mac OS format? HFS+ in short.

If none of the partitions are working.. plug the drive back into the Mac and format it again with a single partition.. plug it back to the AE and check the AE is recognising the disk.. NOT all disks work.. some USB3 disks have issues on the USB2 port of the AE.. sometimes you do need to use a USB hub to help. If the disk is self powered you definitely need a powered hub. The airport does not have sufficient power in the USB to run hard disk directly.

It sounds like you are using the Connect to Server command under the Go menu in the Finder.

The AirPort Extreme should also show up on the left panel of any Finder window under the Locations heading if things are working correctly.

Then, when you click on the AirPort Extreme, the hard drive will appear in another window to the right.

Double-click the hard drive to open it.

Something is wrong if you cannot access the AirPort Extreme hard drive using the Finder. A guess would be incorrect IPv6 settings on the AirPort Extreme and/or your Mac.