Yes, we drove around for 5 days. They drive on the right side. The paved roads and signage are really good, especially since you go up and around mountains all over the place. The dirt roads are trickier, especially when there's a cliff down to the ocean on one side, a blind hill in front of you, sheep on the side of the road, and so much spectacular scenery that you don't know where to look. No off-roads unless you have a 4x4 though.
The (gluteny) bread looked fantastic, and reports from my man is that it was equally delicious (jealous). Didn't see any of this flat-bread you speak of, but did pick up some nice corn "flatbread" crackers for the road.
All I can say is GO! Even if you just hang out in Reykjavik and go on a couple day tours. GO!