You have asked complicated questions I assume in good faith, so I have written a lengthy response. Before I explore your questions, let me repeat and expand on one that I posed to you earlier.
Why is Islamic fundamentalism more popular in certain areas than in others? For example, why is it more common in the Gaza strip than in Jordan? They are neighbors and largely follow the same branch of the same religion. Do you believe it is purely by chance that the approximately two million Palestinians living in the Gaza strip have turned to extremist ideologies at a higher rate than Jordanians?
And note: I don't like Islamic fundamentalism. I don't like any religious fundamentalism. I recognize that religious fundamentalism is a worse problem in Palestine than it is in, say, Sweden. Now, to explore your questions...
How to dissolve Israel of its status as an exclusively Jewish state AND allow Palestinians to return to their homeland WHILE protecting human rights (including LGBT rights) for all people in the land of Palestine is a complicated question. Nobody in their right mind expects it to happen overnight. It is the end goal; the ideal that I believe should be worked towards through political action. In the same way that far-right-Zionist proponents of "Greater Israel" believe that East Jerusalem, the West Bank, the Gaza Strip, and beyond belong to the Jewish people and that the Palestinians are a made-up group that should all move to Jordan. That is their end goal, but they do not expect it to be accomplished overnight either. The Berlin Wall did not fall overnight, neither will the West Bank barrier. Moving on...
Those that do not believe a non-Jewish, democratic, one-state solution could ever be possible generally fall into two camps 1) racialists who believe Arabs are too unintelligent for civilization and 2) people who view Islam as the engine of extremism rather than the fuel. Let me assume you are of the second persuasion. I ask you, what explains the thought process of the ultra-Zionist Orthodox Jew, Yigal Amir, who assassinated former Israeli prime minister Rabin? Is it the mere existence of Judaism? No, of course not, both Rabin and Amir were practicing Jews, so what made one's Judaism murderous? In other words, what led to Amir's dangerous interpretation of Judaism? It wasn't clinical insanity; Amir was sane. To understand what led Amir to interpret Judaism in the way that he did, you would have to understand his particular background and the historical context of Israel. The reason you would try to understand Amir is not to find it in your heart to forgive him, but rather to find and deal with the root of the violence.
The same is true of all religious fundamentalism. The group I am leading up to here is Hamas. The Quran is not a singular force that created Hamas, it is the most ancient factor in a whole list of factors. Factors from the past century include British colonial rule of Palestine after WW2, Britain allowing the foundation of an explicitly Jewish state in Palestine without the consent of the Palestinians, failed Palestinian resistance, multiple resulting wars, the mass expulsion of Palestinians and the ongoing Palestinian refugee crisis, poverty in Gaza and the West Bank, America's history of terrible interventions in the ME (which fuel Islamic extremism in general). When you emphasize Islam over every other historical factor, it is as if you witness a jar of milk being put out in the sun and blame the milk for spoiling rather than the sunlight for spoiling it.
Let us now assume that religious fundamentalism in Palestine is completely removed from the history of colonialism and that Israelis simply have better ideas about civil rights than Palestinians by nature, this still does not excuse the mass expulsion of Palestinian people and the consequent occupation. This line of argumentation is similar to the arguments that European colonialists made when they occupied nearly the entire world (it is no coincidence that Zionism was born during this same time period). Look at British rule over India. Some of their official lines were that they could manage the country better, their culture was more civilized, and that they had a better understanding of infrastructure. These are word-for-word the same arguments that are used to defend Israeli occupation. The British cited their railways, culture, and civil institutions, the Israelis cite their agriculture, tech sector, and civil liberties.
Which is not to say that Israel and British India are the same. How do they differ? One, the Jews that founded Israel suffered in Europe during the 19th and 20th centuries. Unlike the British, they were a heavily persecuted people. Two, Israel is a settler colony which claims that its colonial property is actually its birthright for religious and historical reasons (very similar to the concept of Manifest Destiny). The first point is important and it is understandable how it influenced the rise of Jewish nationalism, but it is not an excuse for colonialism (once again, understanding an immoral action does not excuse it). The second point is so absurd as to be farcical.
One final note to end with, the "pragmatic" two-state solution has become almost impossible today. The Gaza strip cannot function in its current state. It has been aptly described as an "open-air prison". And I'm not quoting Hezbollah here, those are the words of former British PM David Cameron of the Conservative party.. Neither East Jerusalem nor the West Bank are continuous pieces of Palestinian land. They are both patrolled by Israeli military forces and dotted by ever-growing Israeli settlements. Over 600,000 Israelis live in this land that "two-state" proponents claim could make up a future Palestine. Everyone from Netanyahu to Noam Chomsky realizes that the two-state solution is not a solution for lasting peace.