Bike lanes are more hassle than they are worth. You always have to watch for them to suddenly end and then merge back into traffic. I prefer riding in normal traffic lanes. But then, I also live in a moderately rural/suburban area and I stay off the busiest roads, I'd probably feel differently if I were riding in a city.
I would certainly never use the sidewalk, though, that's just ridiculous. A bike is a vehicle, and you should use the roundabout as if you were driving through it.