(1) The judges read the briefs and the trial transcripts (or (1.a)have their clerks read them, really), (2)figure out what they think the answer should be, then (3)go into oral argument usually looking to solidify the position they've decided upon.
The Judges could patent this method of hearing arguments.
There will always be people on both sides of this conflict that are willing to take extreme action to see their side prevail. Usually this is a vocal minority but in the current case we have a Gazan people who are so discouraged and without hope that the majority thinks terrorism is the only viable option. (note: I'm not saying this to defend terrorism - it's still wrong. I'm only saying this in recognition of the fact that lack of viable options is what gets people to turn to terrorism and a peaceful solution will never be found without viable options for the both parties. Of course that raises the question of whether or not viable options actually exist given the extreme and conflicting positions that both parties have laid out... but that's another discussion.)