This is going to sound so generic of me, but it's honestly really hard for me to tell exactly *what* happened, because i can't really see what you're seeing or experience what you're experiencing. It could be dreams, but it could actually be something. Only you really know what was truth. You're not crazy, though.
But... in my experience, if you DO have a gift, you'll slowly become more aware of it over time. If you're meant to have one, you'll be lead into it slowly, as you're ready for it. You'll be guided to learn about what you have and how it works, and it will grow over time. These things have a way of just working themselves out that way. It'll just begin to fall into your lap.
First was just a really scary dream. They seems so vivid and you were even acting the physical parts out in your sleep. So you were border line sleep walking. The other is almost like deja vous. You have seen your mom car pull up a 1000 times before. As you were day dreaming about your mom coming to get you. You imagined you saw her car. Thats all. No big deal. don't freak out and do good in school.
The first thing is pretty dumb. It would have been impressive if you had woken up to find your friend choking or something and you were able to save her. As it is, you had a dream that someone wanted you to wake up, and this turned out NOT to be true. I have dreams all the time about stuff that doesn't happen. Come on.
The second one is a little weird, although I think you're just mistaken about the car not fitting by the buses. But even if you did hallucinate a car driving by, how would that make you psychic? You knew your mom was coming to pick you up; you aren't exactly seeing some unknown future.
You are trying way too hard to think you have some special abilities. If this is the best you can come up with, then sorry, you definitely do NOT have any psychic abilities.
Yes, that's pretty dumb too. You have an overactive imagination. Get over yourself. You have never had a psychic incident in your entire life. If you had, you would have mentioned them instead of this weak bullsh*t. "Ooh I dreamed something and it didn't happen, it was really scary though, I must be psychic!" Dumbass.