Yes. If you are able to hold your baby, you can do skin-to-skin. Tiny babies on breathing machines, IVs, and heart monitors can often be held skin-to-skin. In fact, they often do better in this position: their heart rate, breathing and temperature are more stable.
Most dreaming occurs during the fourth stage of sleep, known as rapid eye movement (REM) sleep. REM sleep is characterized by eye movement, increased respiration rate and increased brain activity. The American Sleep Foundation suggests that people spend approximately 20 percent of their total sleep in this stage.
Normal sleep contains periods of REM (rapid eye movement-dream sleep) during which the brain stem inhibits, or turns off, the motor neurons in our spinal column, preventing any movement except for the eyes. Normally, this only occurs during dream sleep. The apparent reason for sleep paralysis is our safety.