Yes, that's the way ours works too. It burns for around an hour or so and we turn the draft way down once the flames are gone. Then we go back and shut it down completely about an hour or 2 later.

I can confirm that damp newsprint and ashes is the best way to clean glass. I learned that from my mother decades ago and was very pleased to find it worked just as well as I remembered and better than I hoped when I tried it with our stove.