Do bright wallpapers spend more battery than dark ones? I started wondering about this when I realized most websites I visit have white backgrounds, and I know that the screen is usually responsible for most of the battery usage. Since I can't change the background in those sites, I might at least switch my wallpaper to a black one.

Most (all?) phones need back-lighting to brighten the screen when needed. Since that back-lighting consumes battery, is it correct to state that a white screen consumes energy at a faster rate than a black one? (assuming the same brightness level in the settings)

I'm assuming that a white screen needs stronger back-lighting, but I don't know if it's the case.
On OLED, AMOLED and Super AMOLED screens: Yes

LCD screens: No