I've done a lot of reading about sleeping and dreaming in the past. I've had lucid dreams but as I got older, it's the opposite for me now; I'm somewhat awake with my eyes open but can't shake the dream I'm having and think that it's real because I can see it. I equate them more to 'hallucinations' but technically it's something closer to night terrors that I have.
Sleep paralysis is a disorder that I believe is strictly psychological and stems from subconcious thoughts and worries that come out when you're sleeping. I believe in that and night terrors, you don't wake up in a slow progression that lets you leave REM sleep gradually instead of being jolted out of it. My sleep doctor likened my problems more to narcolepsy somehow but I don't know if I believe that.
Everyone dreams, some just don't remember them. Since dreaming typically is a way that your mind copes with the waking world, if you don't remember your dreams, you probably don't need to. There are many physical problems that can cause bad dreams (eating too close to bedtime is one of them) but mostly it's your mind that controls it. And I think there are far more dreams per night than we think, I seem to remember a figure of hundreds of seperate dream scenarios on an average night.
In the morning, your body is preparing itself to come into wakefulness according to your body clock so you don't do as much dreaming as you do in the middle of the night. Which is probably why you remember nightmares vividly if it wakes you up suddenly in the middle of the night-you were interrupted in the middle of a dream so it would stand to reason you would remember it. And I seem to remember a figure of 3-4 hours of REM sleep during an 8 hour sleep cycle. Takes a couple of hours to enter into REM and a couple to come out of it.
Some of this may be wrong, it's been a while since I've had to be concerned with sleep problems and dreaming. But there are some great resources out on the web about it.