There’s just one particular form of mental illness that’s been found to be shared by a significant number of spree killers. It’s depression. At least a tenth of people in the U.S. have it, or have had it, myself among them. And there’s no conclusive causal link between the depression and spree killing.
You are not normal.
There is no normal. You may well be happy and well adjusted. I hope you are. I often am as well. But every single person is neurologically distinct. Normal is semantic, an arbitrary boundary on the bell curve between peak and long tail. Mentally ill, if it means anything at all, just means landing on the wrong side of that arbitrary line.