Anna has Asperger's syndrome.
She always has an "ordinary face", parties aren't her thing, she has trouble making friends, she has a tomboyish appearance (girls with AS often wear boyish clothing because it's more comfortable), she is unintentionally unfriendly, and she sees herself as separate from everyone else, on the outside of the circle. Like many people with Asperger's syndrome, Anna becomes depressed because of her general isolation. She shows improvement by the end of the movie, but it is possible for people with Asperger's syndrome to get over some of their symptoms. Anna's experiences were all just a dream.
She imagined her young grandmother based on stories she'd been told before her death. Marnie was a ghost who came back to comfort her granddaughter.
She saw how depressed Anna was and wanted to cheer her up. Anna has narcolepsy.
That's why she's always falling asleep outside. Anna and the girl she called a "fat pig" become friends.
It happens the following summer when Anna returns to the Oiwas. Anna continues learning more about Marnie to keep her memory alive.
She preserves whatever keepsakes she finds and thinks about their friendship a lot.