I agree that cop should have been unhireable for having been found unfit then lying about it on his job application.
I don't agree about the quick timing of the shoot. The shots were timed based on when Rice
pulled the toy gun out of his waistband, not by some arbitrary desire to shoot quickly.
These cops were told he had a gun. They arrive at the scene. The boy, as you said, could easily have been in his mid teens by appearance. Seconds later, the boy pulls a toy replica of an actual real world gun (a Colt 1911) out of his waistband. In their minds, it was shoot or possibly be shot at.