First story I agree could easily be explained by just having not noticed having taken the keys out, especially since you said you suddenly realized that you hadn't taken them out, not that you saw them dangling from the ignition. And I don't think you would have had to have been having a psychotic episode to truly believe the keys were in the ignition and you were up shit creek. You were under a lot of pressure, basically emotionally battered by your father, and that sort of thing can really fuck with your mind.
Funny thing is, as I was reading the first story, I was already beginning to think about what my reply would be (because I'm a self-centred bastard, of course), in terms of experiences that can't be explained satisfactorily to someone who believes as little in anything supernatural as I do. And the only thing I was coming up with was the series of "deja vu" dreams I've had throughout my life.
It's never happened to me as coherently, and I don't think ever quite as quickly, as what you describe. But probably at least 50 times throughout my life, for as long as I can remember, I'll dream something and then it will happen. Usually it's at least days after the dream, if not weeks or months (it may be years too, but I have enough trouble remembering my dreams for even relatively short stretches of time). And it's never anything important or noteworthy. It'll be a certain view of something, like seeing something on TV from a funny angle, and then I happen to glance at the TV on my way down the stairs and realize I dreamed exactly what I'm seeing, and from where, x amount of time ago. Or it'll be snippets of conversation. The best way I can describe it would be that it's sometimes almost like a snapshot I dream that then happens, or maybe a very short video.
It happened to me recently, when my mum was visiting from Antigua and she and my wife and children and dad and I were all hanging out in the living room, chatting away about nothing important, just friendly family banter. Suddenly I realized that I had seen the entire scene play out in a dream, and recently, and could predict exactly what everyone would say, like we'd rehearsed a script. The skeptic in me wants to dismiss this as all of us just being terribly predictable, and it being easy to guess what everyone would say in any given situation. And that's true to an extent, but this particular time it was so exact that it really stuck in my mind.
I've never encountered someone else who has had anything similar happen, other than the new-age type idiots who believe that EVERYTHING in every dream is meaningful and important, and the secret to accessing it all lies in the healing power of crystals or a careful reading of one's horoscope.
Cool to hear I'm not the only relatively rational, skeptical person who's had experiences like that.