Sugar free or any gum tends to make you hungry, not sure of the physiology but it did for me anyway. Its something to do with chewing and stimulating your gastric juices I think, so best avoided. So now I don't do gum either.
The breath problem doesn't last - its probably best to just drink more water, after a week or so it went for me. You can clean your teeth too - frequently, that helps. But its not a permanent feature of this diet.
GSQ