Zionist in its original sense meant Jewish nationalist, as in a person who believes that the Jewish people are entitled to a nation-state of their own. Nowadays since the Jewish nation-state is a reality the term implies a person who supports that nation-state but there's going to be a lot of differences between Zionists. Some might support the settlers, others might not.
The Hamas problem is exagerrated, its a boogeyman used by Israel to justify the status quo of military occupation and expulsion. Hamas only came into existence in the late 80s and only took power in 2006, if they are the main thorn then how come a deal was not reach in the decades of occupation that preceded the existence of Hamas?
Chase them out how? Will they vote the IDF out of existence? These are all just excuses to justify the continued oppression of the Palestinians. Again, you're basically admitting its the Israelis who can't accept the Palestinians as equals, not the other way around.