Sorry, I'm not following the questions about the "cable box".
To answer the last question first, you can only "extend a wireless network" using wireless if both the "main" and "remote" routers are Apple "n" devices. In other words, the "main Apple router broadcasts a wireless signal" and the "remote" Apple router picks it up and re-broadcasts it, or "extends" the wireless signal.
The Time Capsule (TC) could pickup the wireless signal from the AT&T router and "join" the wireless network, so backups would occur over the AT&T wireless network. But, the TC would not "boost" or "extend" the wireless signal it received. Configured like this, the TC would simply be a wireless backup device. It would perform no routing functions at all on your network.
+My goal is to extend the range of my WLAN and I'd like to relocate the TC to the 1st floor and plug it into my my cable box (which I'm told every box is also a node on the home network).+
This is where I'm confused and don't understand what you mean by cable box. Can you provide more details about this? Do you mean to say that this is an ethernet wall jack?
+Then, enable the uverse wireless functions and have a hard wired connection between the uverse router and my imac while simultaneously being able to backup the TC.+
If you are able to establish an ethernet connection between your AT&T router and the iMac that will work fine.
If you can establish an ethernet connection between your AT&T router and the TC, then all of the devices that are connected to the AT&T router...wired and wireless devices...will be able to backup to the TC. Instead of a wireless connection between the AT&T router and the TC, you would have an ethernet connection. That's a superior setup if that's possible because it's always better to use a wired connection over wireless if at all possible.
If you connect the TC to the AT&T router using ethernet, you could also configure the TC as a "bridge" to "Create a wireless network" using the exact same wireless network name, security and password as the AT&T network. If you did this, then you would increase your wireless coverage by a wide margin. You would have, in effect, a much larger wireless network. Computers would automatically connect to the nearest wireless router.
+I also have a wireless printer that somehow uses the TC as the "mid point" for printing with my imac and PCs.+
If the printer works now, it should work in a new location.
Security wise, you'll be transmitting a somewhat stronger signal, so WPA2 Personal Security should be used on both routers if at all possible and you should have a long, non-dictionary password consisting of random numbers and letters for the network.
Message was edited by: Bob Timmons