Since one of my brown egg laying chickens has switched from one color brown with dark speckles to a different color brown with light speckles, I wouldnt rule that particular possibility as imposable.
My understanding of what makes them brown VS what makes them blue or green leads me to think that would be possible, but I don't think they would be likely to continually alternate.
No, no real color changes are possible. Changes in shade are possible due to when the hen is in her cycle before molt. Brown to lighter brown to tan, for instance.
Red eggs, no, but I've heard of a rare Peruvian breed that lays orange eggs. (that may just mean a dark brown though) Green eggs, yes. EE's can lay blue, aqua, green, yellow, pink, or brown eggs.