"She suddenly left. We don't know why."
It indicates that the action is complete, thus indicating that she is now goneburgers.
I guess in a novel you might see it without 了 to evoke the feeling that you're in the story the moment she leaves. But in a normal situation I feel it's at the very least much more natural with 了 because the action of leaving is viewed as a whole, maybe even with a focus on the result (the fact that she is not here anymore).
Yes, because it signals the change of state has completed. Without it, the translation could be "She is suddenly leaving, we don't know why". Notice that this indicates she's still in the process of leaving.