I have a light fixture to install that is pre-wired with only the black and white wires (see 2nd pic). The box in the ceiling (3rd pic) is plastic and has black, white, and bare copper wire -- the bare copper wire is grounded to a screw in the box (bottom left of picture).
The fixture comes with a separate ground wire (see 1st pic). Also in the 1st pic is the light fixture bracket to connect to the box.
My 2 questions are:
Do I need to use the separate ground wire at all? If not, what do I do with the bare copper wire in the box?
If I do need to use the separate ground wire, does the 4th picture look correct in terms of how to install the separate ground wire to the light fixture bracket?
Yes that looks correct assuming you also use metal screws to screw the canopy to the cross bar and connect the other end of the light's ground wire to the loose end of the ground wire in the box using a wire nut.
The ground screw terminal in the plastic box is meant to help but it is covered in paint and fairly useless. Maybe the metal cross bar is meant to be grounded by contact with that part? But forget that, use a wire nut.
The end effect is the cross bar and canopy, all the metal parts, will be connected to ground.