That looks like the shadow bias for your light is too low. If you are using a movable directional light check if the bias is too close to 0. Your other problem is not an occlusion culling problem, it looks more like z fighting or an aliasing problem due to low resolution or duplicated faces in your geometry (its not clear in the screenshots). Have you tried to see if this happens when using immersive mode? (press F11 while in editor).