Diener des Malers

Each card becomes a new object as it changes zones, so this effect will apply to it from scratch in the new zone. However, replacement effects that care about the color of permanents entering the battlefield (like "[color] permanents enter tapped") will apply to permanents entering if that color was chosen for Painter's Servant because Painter's Servant's effect applies simultaneously with those permanents entering the battlefield. Zone-change triggered abilities that care about the new color (like "whenever a [color] permanent enters" or "whenever you cast a [color] spell") will also work.

If something affected by Painter's Servant is normally colorless, it will simply be the new color. It won't be both the new color and colorless.

The effects of multiple Painter's Servants are cumulative.

This ability affects every card in every game zone, all tokens on the battlefield, and all spell copies on the stack, regardless of who controls or owns them.

This ability doesn't overwrite any previous colors. Rather, it adds another color.

While Painter's Servant is on the battlefield, an effect that changes an object's colors will overwrite Painter's Servant's effect. For example, casting Cerulean Wisps on a creature will turn it blue, regardless of the color chosen for Painter's Servant.