I saw that quote but I don't think he literally means killing though. I took it as he goes the extra mile in beating the crap out of criminals, like the bat branding we see in the trailers. If Batman was a killer, half the characters in suicide squad would already be dead.
Except that's litterally what the word "executioner" means.
As for the SS characters, I had that thought too, but then realized that they've made it clear that the "change" in Batman has been a RECENT thing.
In other words, he's gotten worse since putting everyone in SS behind bars.
Now, I'm hoping that this could be one of two things, one of which I mentioned long ago, before this was even a concern for BvS:
One, Bruce could be going out of his way to let people THINK Batman has gone over that line, utilizing the fear it instills, which is one of the benefits he had more in his early days, before the criminals figured out he had limits.
So I could see him taking advantage of that if the opportunity presented itself in recent years.
Like when Matt goes with it after learning people think he decapitated that guy on Daredevil.
Two, and this also ties into why Bruce is having nightmares with so many allusions to Darkseid, someone or thing is influencing Bruce. It would explain/connect with the dreams, and explain the Omega symbol, Paradeamons, etc, as opposed to Bruce just magically having precognitive dreams.
So, whatever force is affecting his dreams, is also affecting his mind and behavior, hence him acting so irrationally as far as his preemptive approach to Superman.
That said, although I want to have some reasonable explanation for the dreams, I don't like the idea of Bruce not really being himself for the majority of his premiere appearance in this universe.
Although he certainly has more to do in this film relative to Renner in Avengers, Bruce doesn't need to be Hawkeyed in a film he's headlining.