1. "no rain, can't get the rainbow"..i too had a hard time figuring this out. No offense, but sometimes Ayu has awful English pronounciation.
2. I just assumed it had to do w/ the title of the song, "Rainbow". Now that i think about it...hmmm...she ran through all of the spectrum to find herself? remember that white and black are not colors; they are just values. when she was wearing white, may be it means that she found her young, "purer" self.
Personally, i don't think there's supposed to be a meaning behind it. But if you want to watch the video, you can see it at
http://www.youtube.com