Your oxygen/carbon dioxide balance is better with nose breathing.
Teeth need saliva to protect against cavities.
Your partner will appreciate you not snoring!
(you really need to ask the other questions separately...)
I don't know how this relates to paleo but I don't think people have much choice, barring a jaw restraints, once they go to sleep as to if their mouth is open or shut.
I try to sleep with my mouth closed, you never know what someone will try to put in it.
Closed. Mouth breathing even during the daytime is considered "bad posture" for your airway. When sitting upright, your lips should be lightly sealed and your tongue resting against your upper palate. It's even worse when your jaw is hanging open during sleep. Constriction can cause snoring and will shortchange your body of oxygen. Apnea & restless legs could be attributed to not getting enough oxygen while the body is at rest.
Also, mouth breathing has been linked to orofacial defects such as malocclusion and "long face"..
Where sleeping position is concerned, that's highly individual. Sleeping on the stomach, where your neck is turned at a sharp angle really isn't very good for you. But back sleeping, side sleeping, "flamingo" position or fetal--whatever makes you feel comfortable. People change positions during sleep due to muscle fatigue anyway. I use a body pillow for support between my knees when I sleep on my side, and a contour pillow that supports my neck and keeps my spine and neck straight.
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