Yes it is. Since the edges of the holes intersect with the groove, they are inextricably linked. Remove the holes, move the grooves down where you want them and then remake the holes. This is really such a simple model and there’s enough wrong with it that I would probably start over and put the groove in the right place from the beginning making sure to maintain correct layer usage and ensuring that everything is in control.
You clearly need to learn about layers. They aren’t like layers in other programs. Layers are basically just tags that get assigned to components for controlling visibility. Layer 0 is left active at all times. All geometry is created with and continues to keep the Layer 0 tag. Only components and groups get other layer tags assigned to them. Then if you want to look at only the ends of the box, you can turn off the visibility for those components that you don’t want to see. Remember that the only way to keep things separate is to use groups or components.
Yeah. So don’t do that while you are modeling. It masks problems.
As for the mention of style, The Color by layer thing is part of the style. Style is just the control that determines how the model and model space appear. You can choose different styles in SketchUp Free in the Styles panel. In other versions of SketchUp you can also edit the styles to make your own.
You should go through the Fundamentals. There’s a chapter on Layers. Although it’s based on the desktop version of SketchUp, the same things apply to SketchUp for Web. It is really quite simple, though. Leave Layer 0 active at all times, Do not change the layer assignment for edges and faces to anything else. Only assign other layers to components and groups. If you follow those simple rules, it is actually very freeing in your workflow. There’s never any need to chase the layers as you edit your components and you won’t create a mess by forgetting to make a certain layer active before creating new or modifying existing geometry.
I selected the one I moved upward and used the Move tool to move it away from the other one. A big clue that there is something wrong comes when you select one of the side components and the bounding box encompasses the other. You can also tell because when you open one of them for editing, that cylinder is grayed out.
It isn’t critical to be working on the original one. You just need to make sure you are working on the one that is open for editing.
An analogy I often use with my students is that making groups and components is like wrapping a sandwich in zipper sandwich bag. The wrapper protects the sandwich from stuff so if you lay a big pickle on top of it, the juice won’t soak into the bread and change the sandwich. If you want to add mustard to the sandwich, though, you have to open the wrapper first (open the component for editing) and when you finish, you close the wrapper up again. In your case you opened one sandwich and then proceeded to smear mustard on the other one. FWIW, exploding a component or group is tagging the sandwich out and throwing the bag away.
As before the geometry of the holes is connected to the edge of the groove. You can’t separate them without deleting something. The easiest thing would be to redraw the components.
Yes. Or use the Move tool to move the entire groove.
Layers don’t provide separation between geometry. As above, ALL geometry should have the Layer 0 tag. You could fix that by selecting all of the geometry and resetting the Layer association in Entity Info. In order to work on the geometry in any of the components, you first need to open the component for editing.
You can buy me a beer someday. 
