Self-determination. They've been saying that since January of 1976 when we vetoed a Security Council resolution that the non-aligned countries brought forth and would have given them that had we not vetoed it. We vetoed a similar resolution in 1980 and have since vetoed every single time it came up in the General Assembly, all of this despite the fact that there's an overwhelming international consensus in favor of granting them this.
Completely ignoring the reprehensible impropriety of that question, as Israel has not a stitch of legal entitlement to the West Bank whatsoever, those terms are clearly written and have been for over 50 years. This is neither rocket surgery nor brain science.
They occupy Gaza externally. When they say they "pulled out," all they really did was withdraw settlers/settlements and relocated them to the West Bank as settlements rapidly increased after the so-called "Gaza withdrawal." And the withdrawal was not a charitable act, either. They pulled out because Gaza was trending towards uninhabitability. For example, the drinking water is 90% unfit for human consumption. Most of the arable land is gone. But more relevant to your point, the IDF still monitors who can enter/exit, they have the blockade in place, they control the airspace, etc. That's not a real "pullout" in any meaningful sense. Again as Cameron put it, that's an "open-air prison," and since that's the case, one has to know that there's a warden, and it sure as shit isn't Hamas.
1. Hamas didn't "take over," they won in an election that every single international monitoring agency (and it was one of the most heavily monitored elections in history) called "free and fair." Hamas won the election in 2006 because contrary to your apparent perception, Fatah is a group of retched collaborators, and the Palestinian population knows it full well. We aren't as well informed about it because we don't live there. We live in a country whose mainstream media espouses ridiculous talking points like "Saeb Erekat is smart" and "Mahmoud Abbas is a moderate," and we're all just supposed to nod in agreement and not burst into hysterical laughter. And that's not at all to defend Hamas. Hamas is a reprehensible organization. But that's how bad the opposition was, more on that later.
2. As to the issue of rockets, that's hardly a justification for what Israel regularly does to them (mowing the lawn). It's a severely overblown issue off of which even Israel continues to stooge itself. In its so-called "Operation Protective Edge," the MFA reported that over 7,000 rockets and mortar shells were fired and only 1 house in Israel was destroyed. That's because they're not "rockets." They're enhanced fireworks. In fact, Theodore Postol (the MIT professor that exposed the fraud of the Patriot Missile Defense system during the first Gulf War) gave Israel's so-called "Iron Dome" an efficacy percentage of about 5. That is, he estimated that Iron Dome deflected around 350 projectiles which is about half of what the MFA claimed (721, IIRC). Either way, that's a quibble between 5-10%. 40% of the "rockets" were basically duds, meaning they landed in the border area where there was no Iron Dome (because that's only located in major urban centers). And that's not even to excuse the very act of firing such fireworks, but ask yourself a question: what would the United States do if the Zetas fired such primitive weaponry from Nuevo Laredo into Texas? Well they may respond rather strictly, but one thing they very likely wouldn't do is launch airstrikes/drone-strikes/Marine raids/etc to such an extent that it would yield over 100,000 civilian casualties, but that's what Israel did when you adjust the numbers per capita.
3. Like I said, even Israel stooged itself off its own propaganda. When they were trying to scare the living shit out of its citizenry about the tunnels and rockets, people fled and tourism took a nose dive. The MFA then toned down their rhetoric and in some cases would tell people that "everything's OK, you're not being targeted, etc." In fact, Michael Bloomberg went over there shortly after Protective Edge and said that Israel is "safe, and a great place to visit." That's not what you say when you visit a land that's being bombarded by rockets and tunnel crawlers. You say something like that when it's...not experiencing those things.
Again, they're filthy collaborators that only look out for themselves. That may appear to be a "legitimate partner for peace" if the two sides were the whole of Israel and the leadership of the Palestinians, but that removes the Palestinian people entirely from the equation, and I'm sorry that you apparently believe this, but Fatah/The PA couldn't be bothered to give two shits about the Palestinian people. They know that and that's why they enjoy very little popular support.
There's not a shred of evidence to support that claim. They don't even know what those "needs" are and are only concerned about their own wants.
They're already in that position and they have been for some time. If you read Avner Yaniv's rendering of the buildup to Israel's aggression against Lebanon in 1982 (where the PLO was headquartered), you'll notice that one of the prime movers of Israel's decision to do that was, to quote him, Arafat's "peace offensive," meaning his reaching towards negotiating the diplomatic settlement that they'd been seeking for the previous 6 years. The fact that Hamas is in the equation now is irrelevant because they have not at all rejected the principles of the 1988 Algiers Declaration.
There are a myriad of other facts and factors to review, to be sure, but the point is Israel (and the US, if you think it through) has been in a relatively cornered position since 1976 and it's just been excuse after excuse and lie after lie as to why this conflict hasn't been settled, despite the fact that a very broad international consensus supports the very framework of such a settlement, for 51 fucking years.