It is not from the Koran. It is from the variety of hadeeth you mentioned, as well as some mainstream contemporary interpretations of those. Here's a place to start, with multiple sources to follow up with.

A man - singular.

A man is no more and no less than the sub of his life experience. There is no meaningful distinction between Omar Marteen and the set of communities which produced him.

In a society truly free of homophobia, even if he became an unstable murderer he probably would not have picked a gay club. Christian homophobia, general American cultural homophobia, Islamic homophobia. Marteen's murderous hatred of gay men did not pop ex nihilo into his head one day. He was taught it. Those who taught him were taught it. He was the sum of all that, and nothing more.

What exactly is 'moral culpability' in your definition?

Acceptance of or complicity in the beliefs, ideologies, thoughts, and thus also ultimately actions that lead to immoral acts.

How should we punish these people who are 'responsible for the actions' of this individual?

We should not punish them. Compounding misery on misery is pointless.

What we should do is our best to show people why hatred and contempt hurt themselves as well. We should show them how their beliefs, and the behaviour that it in informs, contribute to hate and contempt, which contribute to outcomes like what happened in Florida, while also diminishing themselves.

I emphasise responsibility here because people think there is no possibility of doing harm when they casually wave a text with multiple passages of homophobic rhetoric like the Koran around, encouraging others to read it and take it to heart. Words may have never killed anyone, but they've inspired fools to kill millions.