I'll address the first point in a minute.
Re Arafat, I'm not sure his origins delegitimise Palestinian identity as a whole. Theodore Herzl was a secular Jew who didn't speak Hebrew, he wanted Israel to be a German-speaking Europeanised state. Had it not been for anti Semitism, he would probably have happily stayed the patriotic Austrian he had initially wanted to be. I say this as someone who admires him very much : the point is not to criticise his vision but to point out that modern Israeli Jewish identity is clearly very different in many ways from what Herzl envisaged. Does that make Israel illegitimate?
I've seen bad-faith arguments against Zionism which point out Herzl considered Uganda. This is of course disingenuous because despite being the founder of Zionism, Herzl was pretty untypical of his own movement. To religious, and of course also many non religious Zionists, Zion could not just be transplanted to Uganda (or anywhere else), and they naturally rejected this.
Other bad-faith arguments are that Israeli (as opposed to Jewish) identity is a modern construct, as Israel now has different borders to the ancient one, speaks a language that lots of ancient Israelites didn't speak except for religious purposes (Jesus, for instance, is thought to have spoken Aramaic not Hebrew), comprises people with very different cultures (French Jews, Iraqi Jews, Ethiopian Beta Israel Jews, Karaite Jews etc etc ), and is to a large extent secular. This is clearly wrong and unfair.
Another good example is Ahad Ha'am. He was one of the early cultural Zionists who promoted revival of Hebrew culture. But by his own admission he grew up not particularly connected to Jewish identity, that came later.
I'm not equating Arafat to these people : I don't think he was a positive figure. But I do think that his upbringing isn't really a gotcha that Palestinians are a post-1948 construct.