What does “Not to be a dick, but—” mean? Is “Dickishness” an accepted, stand-alone English word?

There was a recommendation of a new book, How Not to Be a Dick: An Everyday Etiquette Guide in www.Goodreads.com followed by this next sentence:

“On the one hand, nobody wants to be a dick. On the other hand, dicks are everywhere! They cut in line, talk behind our backs, recline into our seats, and even have the power to morph into trolls online. Their powers are impressive, but with a little foresight and thoughtfulness, we can take a stand against dickishness today.

I know the phrase, “every (any) Tom, Dick and Harry” meaning every (any) body, but I’m not sure whether “’dick’ whom nobody wants to be” means, a ‘mediocre,” “unimportant,” “irrelevant to me,” or “officious and impertinent” person, or simply “nuisance.”

Cambridge English Dictionary carries definition of 'dick' only as a man’s genital.

Oxford English Dictionary defines it as 1. (British) a stupid or contemptible man. 2 [mass noun, with negative] (North American) anything at all, beside a man’s genital.

What does “dick” exactly mean when you say “Not to be a dick, but—”?

Are “dickish” and “dickishness” accepted derivatives from “dick,” though I can’t find them in any of Cambridge, Oxford and Merriam Webster English dictionaries?

What would you apply to in paraphrasing “dickishness” in a single word?

The word is commonly used vulgar slang, at least here in America. The derivation is indeed from the usage of dick to mean "penis," and means an arrogant jerk who is horrible to the people around him (the dick is almost exclusively male, probably because of the derivation) either on purpose or because of a self-centered obliviousness.

The word sometimes has a grudging undertone of reluctant admiration for just how horrible the person is.

Dickishness is a playful formation from dick to name the state of being a person such as described above. It would never be used in a formal setting, but it would be commonly understood.

It depends on what you mean by "accepted"—everyone would understand what you mean, but "dickishness" is still a nonce word: a word that has been invented in order to render some concept more easily or efficiently communicable. (In this case, it's a perjoration plus an abstraction: dick becomes an insult, then the insult becomes a quality or an abstract quantity.) It's not in the dictionaries, and it's not appropriate for formal occasions—and not even because of its derivation. Otherwise, I'd feel free to use it, and I'm a Harvard PhD. My dad uses it sometimes.