There was this one scene, I think it was in Athens, when the get cought in a room with hostile PLO terrorists and they claime themselves to be RAF guys. Louis trapped them there. Why did they continue to trust in his intel?
He didn't trap them there. Louis placed them there deliberately, probably at the instigation of his father. As you watched, the two groups spent a peaceful night learning about each other: their cultures, their music, their aspirations, and their hopes for the future. Louis and Papa, apparently both men of conscience (in a very relative sort of way), evidently believed both groups needed this to reach some level of understanding and motive. It was also a very sober object lesson to both groups that they both share the same, small, world. The experience is very telling on Avner, who begins to see his foes as fellow human beings, rather than simply targets. The problem is that it also stokes his growing apprehension over the morality of what he is doing.
Trust has nothing to do with any of this. Nobody trusts anyone, which is why a bunch of well-heeled French anarchiste-poseurs can work for everybody as facilitators; they are aligned with nobody, therefore they are a threat to nobody. Don't break any of their rules, though, like running national intel ops in places they tell you not to, or tip off babe freelance assassins to bump off members of intel organizations. How did that go for her, by the way? And who was it who identified her to Avner?
Do we know that Louie deliberately made two murder squads share a ‘safe house’? Seems like an obvious recipe for disaster, and a surefire way to lose well-paying clients.
If Louie was responsible then why didn’t Avner confront him about it?
Louis is an anarchist who despises the government bodies that help and fund both parties. His actions may seem irresponsible and unduly emotional, but it fits his character and expands the obvious conflicts between Papa and his children (Remember how Papa upbraids them both in the presence of Avner). The plot device, however, is pure Spielbergian fantasy, in order to create a scene where both parties express their wishes.