I have dry mouth and painful gums? Does not having enough saliva makes you get gum disease?

Yes. Saliva tends to reduce bactria in the mouth. When the mouth is dry harmful bacteria will proliferate and cause infection in the gums.
Contributes, yes. A dry mouth is not good, nor is it normal. Unfortunately it can be a side effect of some health issues, and many medications. Saliva is your friend, as it buffers the acids from the bacteria in your mouth. Without adequate saliva, decay and gum disease become more prevalent. See your dentist to help manage this, and see your md to determine the cause of the dry mouth.
Unclear, unlikely. This is a nonspecific finding that may be due to many things. It may be because of too little fluids, or it may be due to a chemical called Atropine which produces, among other things, dry mouth. Gum disease is due more likely to a lack of vitamin c in the diet, which causes scurvy. Even more likely is gingivitis, which does cause painful gums and is due to poor oral hygeine. See the dentist.
Saliva functions. With less saliva you build up more plaque than you did when your saliva flow was normal. The dryness and the plaque can contribute to gingivitis/bleeding gums.