Nuts won't necessarily take you out of ketosis, but nuts are very high in fat and calories (and salt if you are having dry roasted!). Really would avoid them and if you have to eat then have something from the SS+ menu
I would agree with that Starlit_Cazza said. Also, I think that chewing prepairs the tummy to digest food. So suger free gum might be fine, but it might make you feel hungery. You can get sprays if your woried about your breath.