The bad guy holds a gun to the child’s head multiple times. At one point he pulls the trigger while the gun is positioned on her head and pulls the trigger but the gun has malfunctioned.
The girl is beaten up by bullies as robots hold her down.
Not in a gory sense, but a repeated gag throughout the film is people closing doors on a dog’s face or head. This happens over and over, though only once is it explicit that the dog was hurt by it.
A human body controlled by a robot continues moving after having fallen off a tall building, and bones are clearly broken despite his mobility. His arms hang at bad angles and at one point he has to hold his head up with his own hair because his neck can’t support it.
I completely missing the part where you're shown that the father died, so it must be shown only briefly. From the dialogue the dad might just as well have left his wife and daughter. --- Added later: On closer inspection, there are two stills in the intro sequence photo montage of the mother and daughter standing by a grave (we don't see the inscription on the headstone).
A villain falls from a great height but continues walking on broken bones, so his limbs and head hang at disturbing angles. There is also a moment when his eye comes out of its socket, revealing it to have been a synthetic eye despite appearing real. Both the socket and eye are shown.