Safe Passage prevents all damage, not just combat damage, that would be dealt to you and creatures you control this turn.

Safe Passage will prevent damage dealt to creatures that weren’t on the battlefield at the time it resolved.

Safe Passage doesn’t prevent damage that would be dealt to planeswalkers you control. Although it can’t prevent combat damage that would be dealt to your planeswalkers, it can still prevent noncombat damage that your opponent would want to redirect from you to one of your planeswalkers. Just apply Safe Passage’s prevention effect to that damage first, and there won’t be any damage to redirect.

Safe Passage has no effect on damage that’s already been dealt.