Brushing teeth before receiving Communion is fine; in fact, it is highly recommended. We owe it to Jesus out of respect to receive Him with a clean mouth (and clean hands, if you receive that way).
Gum-chewing is a different story. It is usually done because it is pleasurable (flavor, mouth sensation, chewing activity). I think in the spirit of fasting it would be good to abstain from it for an hour. (An hour before Communion is usually about fifteen minutes before Mass starts; anyone should be able to do without gum for an hour.) I’m not sure about the letter of the law; I think only water and necessary medicine are permitted. Some gum has nutritive value (sugar), but that might be splitting hairs.
The absolute worst is when people approach Communion with gum in their mouths. I think that is terribly disrespectful. (Disposing of gum under the pew ranks right up there, too. Yes, it happens.)