1) "empty pipe": If you're using a double-action semi-automatic, you can carry with a bullet in the chamber - which means all you have to do to fire it is pull the trigger. This would be similar to most revolvers.
OR you can carry with NO bullet in the chamber, which means that before you pull the trigger, you have to "rack the slide" (pull back and release the thingie on the top of the pistol) to get a bullet into the chamber.
2) "Shoot to kill": In my department we are taught "shoot to stop". BUT we are also taught to shoot to the center of mass - which, I suspect is likely to kill or to permanently disable.
As far as killing goes, I'd prefer to shot Mozambiques - two to the center of mass and one to the head. As far as "Stopping" goes, I'd like to research shooting to the pelvic area, which some claim is a guaranteed knockdown and NOT necesarilly a killing shot, or even a permanently disabling shot (though one is coming mighty close to Mr. Happy, I guess).
As for keeping one's finger on the trigger, I don't know where that comes from. We are trained to keep the finger OFF the trigger unless you have decided to fire.
As for looking and discovering that one's gun is cocked, we are trained (and I practice) to decock before holstering every time. Also, my duty holster won't work if my Sig P226 is cocked.
My other duty gun is a S&W 686P and it's a double action revolver. It isn't cocked unless I cock it, and after a trigger job it's so smooth in DA that I don't ever cock it. (Well, okay, maybe at the range when I'm showing off, but I practice double action nearly all the time.)
As far as special souped up weapons are concerned, I have had trigger jobs on both my duty guns, but other than that they're stock guns. I don't know any cops that have souped up guns. I do know one department that has stock, double-action-only H&Ks, and I know of other departments that have "double action only" automatics.
But I also wonder how much difference that makes. When I shoot in competitions (where I usually come in last in terms of speed, but do okay in accuracy) I don't even notice if I'm firing double action or single action. When the clock is running and the adrenaline is up, I'm all about sight picture and "squee-ee-eeze the trigger".
Yeah, some LEO's are dopes. Lots aren't. My guess is, on average, you get what you pay for.
And final word: I wish more of us knew how to act, especially how important it is to keep your hands visible and to avoid sudden movements, when firearms and adrenaline are in the same area.