Yes the back diaphragm plastic cover is missing the white idle screw but you can put a later cover on without the idle screw.
The silver disk on the diaphragm locks the diaphragm to the poppet valve so it should have this or some sort of clip.
The idle screw won't slow the idle if it's missing and it's running too fast ,if the motor is in good mechanical condition then it may just be the carby parts have worn and to fix this you add a brass washer to hold the poppet valve in a more closed direction to bring the idle down.