All my measurements stay at 0

The Lightstone is not reading you properly. Most likely you have the finger sensors on upside down (make sure the double latches are over your fingernails)

All my measurements stay at 0 except for Absolute Skin Conductance, which is below 2.0

Your hands are too dry (try applying moisturizer on your fingers before using the finger sensors).

Why does the Absolute Heart Rate measurement suddenly double or halve?

If you move your fingers you can create false heart rate measurements (finger movement artifacts). Also if you are cold or have poor circulation the Lightstone may have trouble reading your heart rate. In either case faulty readings appear as the heart rate jumping directly to about twice or half its value (from 50 directly to 100 beats per minute for example). Try keeping your fingers still, putting on a sweater, or turning on the heat in your home. You can also warm your hands by relaxing, as relaxation tends to lead to warmer hands through increased blood flow to your hands and feet.

All my numbers change except for Heart Rate Variability, which stays 0.

The heart rate variability number will not change from 0 until you enter a relaxed, calm, positive emotional state. It can be the most difficult to change (impossible to change if you have a pacemaker). You need to make the increase and decrease of your heart rate smooth and rhythmical to increase heart rate variability. Try the relaxation techniques. The defaults of Inner Tube and Particle Editor are keyed to primarily respond to this very important reading.