Non-REM is the stages 1,2,4 in sleep... The deep sleep, where little dreaming occures.
People who sleepwalk/talk do it in N-REM
Non-REM simply means Not having Random Eye Movement, your in deep sleep.

And yes people who are really good at meditation can hallucinate or have visions. It's extremely difficult it takes years of practice...

The best you can probably hope for is doing it naturally like you are now... find something that keeps your eyes closed.

Some people can just slip into a hypnotic/trance state easily... some don't.
Just depends on how Passively Attentive you can be.

-Daniel