How is it possible that I have never had a nightmare, when I dream I am fully aware of it & can alter any dream I think is stupid or just turn my head slightly to end it, yet I can remember little of what I dream? I also have dreamed things with such imagination & technology too advanced for my education as well as a few reoccurring dreams in my youth that actually happened 15 yrs later & I was in awe as it was happening because I could recall each event as it happened.
Sleep itself is still not very well understood, dreams even more so.
But there does seem to be an association with memory, with sleep being a time where memories are sorted and some are “purged”.
This both explains why we dream (because the consciousness tries to make a “story” out of these random memories flashing by), and why we don’t tend to recall dreams very well (because our memory centres are performing a different kind of function).
On some of the more specific points:
This is called a lucid dream.
Did you record the dreams in some sort of dream diary? And further, did you try, at the time, to state what prediction you thought the dream was making?
Humans have a confirmation bias with such things; we will latch on to things which appear to match and ignore the many things that do not.
TBH I wish dreams were predictive, as I used to have awesome dreams 
Dreaming is damn weird. I am a semi-lucid dreamer: I can sense a nightmare developing, and act to avoid it. I can “go down the other path” so to speak.
Many people have solved problems in their sleep. “Sleep on it” before making a decision can be very good advice. (It doesn’t always work, of course.) I’ve solved math problems in my sleep.
As for prescience and precognition, most of us here are skeptics. We’d have to see some very serious documentation of dreams that actually predict future events. Remember, you have a LOT of dreams. If you dream about, say, meeting a beautiful woman at the local Art Museum, and then it actually happens, you have to factor in the dreams where you meet a scary dog at the ball park, or where you meet a mugger at the convenience store, or where you meet a policeman at the pharmacy. Given the large number of dreams people have, it would be more surprising if none of them eventually came true.
Meanwhile…try to dream about winning the lottery! If you don’t win, no harm. If you do win, it provides further evidence about dreams coming true, and you’re rich, too!