Let see, so first of all it is redundant. It is a piece of webbing that is wound around itself. It is also sewn around on each side as well as bar tacked. We have tested some of these by just duck-taping them together. The start to disassemble around 3000 lbs. of force. (slow pull)
Belay loops are the strongest part of the climbing system. Even the weakest belay loops we have tested blow at about 8000 lbs. of force.
After the Todd Skinner accident there was much testing on belay loops done. One test in particular was cutting the belay loop 90% of the way through and then pull testing to failure. It was holding around 700 lbs of force.
I see people all the time putting this extra cord to "back up" their belay loop. The problem with this is that it is cluttering up your "work space". I have seen someone accidentally clip into their "backup" cord only. To put this in perspective a 6 millimeter cord can only hold around 1500 lbs of force. This is only twice what a 90% cut through belay loop can hold; so not really nessasary and can cause more problems than it could ever help.
As for backing up the Figure 8. There is no need. This actually has been found to cause more problems than it could prevent as well.
The reason that we only use one carabiner to belay is that it is right in front of us and easy to inspect. You can use 2 with an atc, this just adds friction.
Same for the rope (unless you are using doubles) we should be inspecting this as we belay.
Take every thing off your harness at the end of the day and inspect those belay loops and you should have no worries!