Alice was put in an asylum most likely because she "saw" things in the future, like she does in her vampire state. Someone (either Carlisle or Edward) said that usually if a vampire has a special power, they had a trace of that special power in their human life. Like how Edward was able to read people's faces, and now he's able to read people's mind. So Alice was put in an asylum, and one of the asylum workers, a vampire, created a special bond with her. Not romantic, but a special bond. Then when James caught her scent, he instantly wanted to kill her, so the asylum worker bit her and made her a vampire, thus protecting her from James. So James killed the asylum worker out of revenge.
Oh, and Alice and Edward were NOT destined to be together, and nor were Edward and Rosalie. Rosalie was just mad that Edward didn't want Rosalie, because she was a very self-involved, beautiful, but self-involved:) person.