You are more likely to remember scary dreams because you are more likely to wake up. Forgotten dreams are the result of the conscious awareness not engaging during the dream.
I had night terrors from the time I was very young and actually into my early 20's, with decreasing frequency. This left me with the habituated pattern of waking up in the middle of the sleep cycle regardless of dream content. So for many years I remembered most of my dreams every night. In addition to the nightmares, I've had lots of action-packed dreams. I generally think most dreams are like housecleaning your mind--you come across something and reminisce about it, activate the imagination, etc. then move on. So dream content can change radically with changes in what's going on in your waking awareness. I also think that some dreams come from spirit rather than from mind, but that's another conversation.
Continuing a dream is not necessarily a form of lucid dreaming; you can do it intentionally or unintentionally with lucid and with non-lucid dreams. It's basically a matter of keeping your mind in the same state as the dream. This happens more easily with scary dreams because the fear bubbles over into the waking state. Not fun when you keep slipping into the same nightmare each time you wake from it. On the other hand, I've done it intentionally with interesting dreams that had a long story arc.
As for the final question, I have had experiences like that as well. What I refer to as night terrors were mostly that. There is a phenomenon called sleep paralysis or from folklore, the "Old Hag" that describes this experience. There's a physiological explanation, and there's a paranormal explanation. Whichever you choose to describe your own experience is up to you, but it's damn scary either way!
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