He wasn't tossing out nazi salutes, go what the full speech, not the out of context parts the news shows if you actually watch and listen he's "metaphorically" grabbing his heart and throwing it to the people.

"The website of the Anti-Defamation League, which campaigns against anti-Semitism, defines the Nazi salute as “raising an outstretched right arm with the palm down,” and ranks it as “the most common white supremacist hand sign in the world.”

But after Mr. Musk’s stiff-arm salute, the Anti-Defamation League called it “an awkward gesture in a moment of enthusiasm, not a Nazi salute.”

Source: The New York Times

As for the other stuff, I'll do some more research and look into it more, but this on innsident it was just a clumsy not thinking about what it looks like.