It is possible to fall into REM sleep at night if you have taken a longer nap during the day. I think it's around 5 hours until you will start the normal sleep cycle again.

SP is more likely to happen when you "mess" with your sleep pattern, like taking longer naps during the day when you're not used to it. I've had SP once, and it was during such a nap.

Not sure what to answer to your last questions, though.