This will be a lengthy post, but I hope it proves helpful!
For starters you need to realize that in SketchUp a Layer is a thing that an entity (a SketchUp drawing object) can reference to decide its visibility (and color and as of 2019 dash pattern). The effect is similar to the hidden attribute of an entity, but hidden is object-by-object whereas a layer controls multiple entities’ visibility at the same time. Almost anything that shows on a SketchUp drawing view can refer to a Layer to decide its visibility - edges, faces, groups, components, dimensions, text, …
The phrase “on a layer” comes from traditional 2D CAD and image editing, where layers combine the visibility control of SketchUp’s layers with the gathering/structuring control of SketchUp’s groups. To reiterate, in SketchUp these are two separate behaviors controlled by two separate constructs. I prefer to say an entity “uses” or “associates with” or “refers to” a layer, because that captures the idea that the entity points at the layer not the other way around.
Using different layers for edges and faces is a bad idea because SketchUp’s layers don’t prevent them from sticking to each other or intersecting. Sure, if they are spatially isolated (e.g. if you draw the second floor at a different height than the first floor or draw one object off to the side of others) they can’t interfere. But that’s because they don’t overlap, not because they use different layers! The risk of mixing layers on edges and faces is that when you modify edges that are visible you may be also altering attached ones that are not visible! That’s a quick road to madness, and is why the guru advice is to always draw edges and faces using Layer0 and leave them that way.
A group (or component - for simplicity I’ll just write “group” but everything applies equally to components) is an entity that gathers together several “nested” objects and isolates them in their own context so that they won’t “stick to” or intersect with anything outside the group. Edges and faces inside a group can still affect each other, but can’t affect ones in a different group. An entire group can be (for example) repositioned using the move tool without needing to grab each of its individual contents.
So, Layers and Groups in SketchUp are completely separate ideas.
On to your specific questions:
From what I wrote above, you may be able to see that this is not really a very meaningful question as layers aren’t “within” groups or vice versa. In fact, multiple groups can use the same layer - including groups nested inside different outer groups. You should always gather the pieces that you consider to make up a single object into a group, both so that you can manipulate them as a unit and so that they are isolated from other groups of pieces.
Usually you would consider the second floor to be independent of the first floor so that changes to one don’t automatically alter the other. For example, if you move a second floor wall over, you don’t necessarily want to warp the walls below it on the first floor. So, you would want them to be separate groups. But, you would very likely want to gather smaller collections within each floor for the same reasons. You also gain semantic power by such grouping - e.g. the bathroom can be a separate thing from the bedroom, not just one big mess of walls and floors.
Now, layers can in principle be used by both a group and its contents. But if a group’s layer is not visible, its contents will not be visible regardless of what layer(s) they use. It wouldn’t make sense for a thing’s contents to show if the thing itself is hidden!
Going the other way, it can happen that you want the thing as a whole to be visible but just some of its contents to be hidden. That would happen if the group’s layer is visible but the contents use other layers that are not visible. With a few special exceptions, you usually want an entire “thing” to be visible, not selectively some of its edges or faces, so when this behavior is needed you create another group nested inside the overall group, and set it to use a layer separate from the one for the overall group. For example, you could have two alternative sets of plumbing in nested groups of a bathroom group and by having them use different layers you can toggle visibility between the alternatives.
Again, the idea is that the groups are what make them separate “things” and the layers are what let you control which things show in the drawing.
You just assign the group to use the new layer and leave its contents alone (and yes, he did mean layer0).
New objects, including groups, are automatically assigned to use whatever is the currently “active” layer in the layers window/tray. Ordinarily layer0 should be left active during all drawing operations, including creating groups. That way you don’t have to remember to switch back to layer0 before drawing additional edges and faces. In entity info you can tell the group to use a different layer later if you need to.
The group changes to referencing the newly selected layer. Nothing else about it or its contents is affected.
Edited to correct “model info” to “entity info”. Good catch @DanRathbun