On devices with OLED screens, the more pixels on the screen are lit up, the more power the screen consumes. So on the majority of smart phones these days, dark mode will slightly reduce energy consumption. Devices with LCD screens will likely show no difference, and we're talking a fairly negligible amount of power here anyway.
That's absolutely not true. OLED pixel energy usage is proportional to the amount of light they need to emit. Dark gray is essentially the same as black in terms of energy usage.
Not exactly. Yes dark grey will consume more power than full on "the pixel is turned off" black but it does take less energy to show a dark grey screen than a bright white one.