First, there should be a few little hints in the score to help you. look for the letters "md" and "ms". "md" means right hand, "ms" means left. Brackets like [ across staves means the same hand should be used for all the bracketed notes.
1. Why did the composer (Edvard Grieg, genius) write the notes out on three staves instead of just two?
2. In the case of two m.d. staves: How are you supposed to keep the notes on the top staff tied together while moving the right hand to play the notes on the 2nd staff? (I use the pedal!)
I believe they think it makes it easier to follow. Some people agree, though I think otherwise.
I think Bach thinks otherwise as well and he died long before they were even born.