I don't know about predicting the future, but I will say that I experience deja vu on a very regular basis. I've had similar experiences to you in which I will have a dream, and I can recall that dream in the morning. Then months, sometimes years later, the event will happen exactly as I dreamed. These dreams are very different from my normal dreams as my regular dreams are full stories seeming to last hours while the deja vu dreams are less than a minute long. Also, while my dreams never tend to get too weird, in most of my dreams I act as a fly on the wall or very neutral while in my deja vu dreams, I will act like I normally do. Hell, often times in the dreams as of late, I will actually say "Hey, deja vu!" in the dream.
When I was younger, they tended to be just images like if I had taken a picture of that moment. I remember a couple I had were seeing a certain book in the library or getting a new mattress. As I got older, the dreams became longer and while the earlier ones were silent, they know have sound, usually conversation. When I'm experiencing deja vu, I know what they're going to say before they actually say it. It's a very odd feeling. But they're never about anything important, but it's not events that are totally commonplace in my life. For instance, I've never gotten deja vu while eating toast, but maybe I'll be having a conversation with a friend, and I suddenly know the next three or four lines of dialogue.
I don't know what this implies about the future, but I will say I don't buy the memory processing theory. If it was true, why can I recall the dream when I wake up instead of only after I get the sensation of deja vu?