There was once a time when the Israelis and Palestinians have coexisted in relative peace, what happened ?
there are a lot of components, but i'll try to give you the short version.
in the early 20th century, Russian and some European Jews began to migrate back to the area known as Palestine. this is the biblical and historical site of the nation of Israel. there were not many Arabs in the area because the land sucked. the Jews that came in and the Arabs that lived there did work together to reclaim land, build stuff, etc. the area was controlled by the Brits and no one really cared about it.
post ww2, the Brits agreed to turn the area over. the Arab countries were directed to divide the land 25% to Israel, 75% to the "Palestinians". at this point, i put Palestinian in quotes because there were a bunch of Muslims in Jordan, Egypt, Lebanon, and Syria, who had decided that the Arab countries needed to be united as the nation of Palestine. they called themselves "Palestinians" and they were a real problem for the Arab countries. (and Egypt)
the Arab countries needed a place to dump these people. at the same time, they were really ticked off that Israel had successfully established itself. they promised the entire area of Palestine to the "Palestinians" and other Muslims, and attacked Israel. that didn't work well. they were left with people they needed to dump. no promised land to dump them. bad PR after losing to a piddly little bunch of Jews.
the Arab countries also had a growing terrorism problems in their own countries. the Islamist movement was growing and it was aimed at Arab governments that were deemed "westernized". the solution for those Arab countries was to use the Palestinian plight, which these governments had helped create, as a distraction. they pointed the terrorists at Israel, and countries that supported Israel. out of these groups came the leaders of Al-Qaeda and all those you mentioned.
that's a pretty abbreviated history, but.....