1. The UN did not establish Israel. They passed a nonbinding recommendation to create a two-state plan, which would create a Jewish state and an Arab state. That passed on November 29, 1947. The plan never went into effect as a civil war immediately began, and Palestinians did not support any partition.

As for how they arrived in what became Israel, it was primarily through immigration legally, not violence. They legally bought most of the land they lived on. There was more illegal immigration between 1939-1948, though not violent, due to restrictions on Jewish immigration imposed following the Arab revolt of 1936-39 (the British sought to calm Arab anger prior to the coming war, WWII). There was violence, but it was not used to take land. The British were in charge of the area, after all; the land wasn't a free for all you could just grab, and there was rule of law. But the violence between Jews and Arabs flared periodically, most often in rioting like the Arab riots of 1920, 1921, and 1929, or smaller incidents along those lines.

2. The Palestinian (and when I say that, I mean Palestinian Arab; at the time, Jews were also considered Palestinian) response was anger. Palestinian Arabs sought to prevent Jewish immigration, viewing it as a threat to their ability to get an independent state in all the land. They were also upset because often, Jewish landlords would take control of land by buying it and asking that the previous owners make sure it had no inhabitants. Those leasing land would therefore be asked to leave or bought out, and sometimes became poor. While this didn't necessarily cause mass homelessness or anything like that, the bitterness led to a sort of national consciousness of the dispute and therefore it became a bit more salient.

3. Some left voluntarily, some were forced out. Benny Morris is one of the biggest experts on the subject, and he supposes that around 710,000 to 750,000 Palestinian Arabs lost their homes (we're leaving out Jews in this count) during the war. He estimates that up to June 1948, around when the Arab states invaded the newly formed state of Israel, the vast majority of Palestinians fled in fear. This was encouraged by some of the smaller militias in particular (Irgun and Lehi) who committed atrocities with the intent of getting Arabs to fearfully flee. There was some evacuation of Arab populations, but that primarily took place later and wasn't the biggest cause of the exodus. There was also the problem of some Arab propaganda that exaggerated actions by the Jewish militias, with the hopes that it would encourage Palestinian Arabs to stand and fight, which had the opposite effect. Up to June 1948 less than 10-15% of the Palestinians who left were expelled; most fled. So, judging by the fact that half of Palestinians who left, left before June 1948, a total of around 7-8% of all Palestinian refugees during the war (from 1947-1949) were expelled. After June 1948 through to the end of the war, around half of the Palestinians who left were expelled. That means the total is somewhere near 30-40%, depending who you ask, when you look at all Palestinians who left during the war.

So the majority fled, but expulsions were quite common as time went on. They were not Israeli state policy, but individual commanders made their own decisions, which meant southern command would do something quite different from northern command based on their desires and their military assessments.