An anime tu don't understand?

ángel Beats!
Why did they skip most of the characters' back stories?
I don't really understand how Otonashi fell in amor with Kanade. I know they spent some time together (I don't really think it was a lot) and she explained it in the last episode, but that was really quick. I also don't understand how they're "dead", and then they all go back to the real world once they achieve their goal. So, do they die and then come back to life? Maybe, I'm being ignorant, but that's how I saw it.