Why does Daru give the Arab the opportunity to escape? Why doesn't he escape? Why doesn't he take the road to the Arab lands at the end of the history?

Daru is sympathetic to the Arab prisoner and, like liberal French Algerians in general, to the Algerian independence movement, though Algeria is felt by Daru to be his own true home. He doesn't like the idea of the gendarme, Balducci, handing the prisoner over to him and, understandably, does not want to be responsible for the Arab's incarceration, because he has no way of knowing if the man is guilty of what he's been charged with.
Why it is that Daru sees him walking toward the East, on the way to prison, is an open question. It's emblematic at once of man's taking responsibility for his actions (if indeed he is guilty) but also of the free and irrational choice man is always faced with. In Camus's fiction, man makes decisions not so much as expressions of rationality, but because, by asserting his will, even randomly, he is creating the values which otherwise are lacking in the universe. The same can be said of the decision Daru makes in not escorting the man all the way to prison.
Though Daru has felt sympathy for the prisoner and has acted on that feeling, the message he finds on the blackboard in his schoolroom is a metaphor for the fact that regardless of what choice one makes, there are consequences. In the conflict between the French and the indigenous Algerians, there was, as in life overall, essentially no exit, if we may borrow the title in English of Camus's friend Jean-Paul Sartre's play.