Watermarks are contained in styles. There is always a style associated with a scene. Your problem is that you have more than one scene using the same style, so they share the watermark. You can see this if you open the styles window and watch how the selection changes when you change from scene to scene. For example, scenes Start Here, 1, 2, and 4 all use the style named “Style” and scenes 9,10,11, and 12 all use the style named “Style 8”.
Regarding layers, you have two issues.
First, you have many ungrouped edges and faces that are referencing other than Layer0. That is a risky practice because SketchUp layers do not prevent edges and faces from sticking to each other or intersecting each other, even if all but one layer is non-visible. This situation won’t cause issues provided the edges and faces are always located in different places in the model (so they can’t stick or intersect anyway), but will cause unexpected results when they overlap. Put edges and faces into groups or components to protect them against interaction with ones from a different object.
Second, you have edges and faces inside a group/component referencing the group’s layer instead of Layer0. That’s not usually necessary because when the group’s layer is non-visible, all of the group’s contents will be non-visible regardless of what layer they use. But if you ever get contents of a group using more than one layer, you can get the same issues as described in the first item above plus strange cases in which not all contents of a group become visible when you turn the group’s layer visible.
So, to avoid problems the advice of all SketchUp experts is to draw all edges and faces with layer0 active and to leave them there until/unless you are yourself expert and really understand the consequences!