One thing I still don't quite understand is the whole swapped identity thing. The two girls didn't swap identities, right? Grandma's who she says she is, despite the Alzheimer's?
No they never swapped identities. Their personalities just changed because of their experiences. It seemed like they swapped personalities because they swapped outlooks on life.
Mitsu used to be cold and reserved because she felt trapped by society (she was in an arranged marriage). That was changed when she met Kiyoko who inspired her to live the life she wanted (which was kind of a double edged sword since she took "living for Kiyoko" a lil too far lol and was never able to move on). So Mitsu ended up living with more determination and courage to face society.
Kiyoko used to be outgoing and cheerful because she thought she'd be free from society's rules if she died. So she lived her life cheerfully thinking she will die soon anyway. After the suicide failed, she realized she'd have to participate in society and lost the courage to break free of it and thus became depressed and resigned. Being too afraid to live the life she wanted and at the same time too afraid to take her life, she just withdrew into her shell.