Was wondering if you don't eat for 24 to 36 hours do you start to experience severe dry mouth and feel really tired?

Yes. : Not a good idea to do this. It can be dangerous to your health.

Yes: You can definitely feel tired because your body is running out of easily accessible nutrients. Are you drinking water as well? If not, you should. You need a lot of water daily to keep your cells working properly. There are better ways to diet than this one, if that is what you're trying to do.