I will give the ethological true reason for why Trump could shoot someone in the middle of 5thavenue, “or whatever,” and never lose a single supporter.
And give my generalistic “ explanation[s] to describe Trump’s irregular mental state.”
1) For the killing on 5th avenue:

Donald Trump‘s supporters know him mainly from “The Apprentice,” an alternate reality in which he represented the ultimate uncriticizable authority.
There is an aspect of the natural world that explains there fixation: The “agonistic behaviors” that social animals use to establish their dominance while growing up. During their youth, indeed, all males compete among themselves using display behaviors (The Apprentice) involving “tests of strength or threat display that make animals look large and more physically fit, a display that may allow it to gain the resource before an actual battle takes place.” Agonistic behavior — Wikipedia
This last sentence in bold was an epiphany for me: for Trump’s supporters indeed, it doesn’t matter what he does in the “actual political battles” of the day, The Apprentice has already for them confirmed him as an uncriticizable winner!

2) My generalistic explanation to describe Trump’s irregular mental state:

Trump is not a liar. He’s a prolific builder of “alternate realities,” without which he could not function since he has lived in such realities all of his life. Firstly, in the one his daddy effectively built around him. Then, the one his lawyers professionally created while managing his business failures in ways that made him perceived his bankruptcies as genuine successes while others were suffering the consequences. Then, the one created in his TV reality show by professionals producers who staged him as an implacable and ruthless dominant figure.
Now that “the buck stops with him” he cannot but openly creates himself his own alternate reality while awkwardly trying to be as effectively professional and creative, as his daddy his lawyers and his producers were respectively.
And, he is surprisingly good at it; nobody I believe in the whole world could have done what he did and do what he does and still comfortably be in power. Too bad he doesn’t put his true dominant personality at work to “make humanity great again,” like we need to become before we destroy everything we have created…

We need to convert our economy and our mind. I have been working at it for forty-five years as a learned-generalist of science with two general BA and one unspecialized MA in ZooAnthropoSociology. I will soon, I hope, publish on the Internet — our “budding” collective self-consciousness — the result of my research in an undefendable (I have no peers) PhD dissertation. However, it will be understandable by all honest mind from 9 to 99, and provisionally title: Know Ourselves!: Defining the Present Existential Problem of Humanity in Evolutionary Terms, in which I describe our species as an individual in dire need of developing a collective self-consciousness to function adequately in nature, like “terrible twos” individually need to do with their self to function adequately in society.

Let us hope that Trump can convert himself. At the moment given the state of the world, I believe that if he does convert himself and grow out of his own “terrible-two” stage that he could be hope for humanity.
PS I will publish this response in Medium under the title Explaining the Trump Phenomenon in Evolutionary Terms.