The chaos ability isn’t a mana ability. It uses the stack and can be responded to. You choose the color as the ability resolves. Once the ability starts resolving and you’ve chosen a color, it’s too late for anyone to respond and change your devotion to any color.

A player’s devotion to a color is equal to the number of mana symbols of that color among the mana costs of permanents that player controls.

Nyx’s first ability will apply to nontoken creatures from the moment they enter the battlefield. Notably, a nontoken creature entering the battlefield will cause the constellation ability to trigger.