Murray did absolutely nothing wrong

Similarly, I wonder why Arthur killed his mother, he loved her

I agree, he was just busting Arthur's balls, which is what comedians do. It was nothing personal. But I guess the point was to show that Arthur had been abused (both verbally and physically) by the world so many times that he was hypersensitive towards any slight made against him, and it was just that much worse when it came from one of his idols.

I think we are supposed to see the scene as a jab to our present day mainstream media.
Murray's team should have fact checked if the guy had some condition or not but as is the case today ,the race to get more clicks , more ads and more money , so does Murray wants more viewers who translates in more ads and so more money for him and the TV station.
At the end of the day he just doesn't care as long as he gets to do his things and Murray just doesn't give a f*** about anything other than the means that make him stay in business.
Just like in our world where fake news and clik-bait articles are shown everywhere regardless if it's the truth or anyone has to suffer, after publishing them.
It's no wonder mainstream media didn't like the film as it made themselves look in the mirror.
Example : the amber herd johnny deep case . The msm never cared about the truth and after recent developments they are trying to sweep the case under the rug because it paints them as morally bankrupt, unreliable and a cesspool who would do and say anything for a buck.

It certainly didn't warrant murder, but by the time Murray gets shot , Arthur is pretty much insane and few things make sense to him.

Yes, he did nothing wrong... nothing that should have gotten him killed anyway.

But harmless humor or not, the fact is Murray did use Arthur. Perhaps Murray had no knowledge of Arthur’s disability, however at the end of the day the likely main reason he invited Arthur to his show was so everyone could laugh at him (he didn’t expect Arthur to suddenly make audiences laugh). Also, Murray honestly did wrong by not cutting the interview when he was signaled to do so near the end — good tv was a priority!

That being said, Arthur is... not the most sane guy around. Most of what you said would make sense except we’re talking about a person who really went off the deep end. “All I have are negative thoughts.” Being a hypocrite would be the least of “Joker’s” problems.

Arthur wasn't supposed to be a sane, rational man.

Arthur also acted in self defense on the train ... for the most part.

Who did Arthur made fun of or laughed when Murray made fun of someone? Don't remember anyone.

Murray used Arthur like a bear on a hot plate. Fck him.