Michelle, more questions are certainly OK.
You're right. It is sometimes unavoidable that faces get split. When they do, however, that is your clue that the outer edges are no longer planar. If you were to build the structure with a plywood skin, you could probably torture the plywood a little, bending it to screw down the perimeter but it would be stressed that way. Obviously if you carry that too far you'll either break something or have to divide the panel into smaller pieces.
In SketchUp a face must be flat. There's no bending a single face as you could with plywood.
As far as fixing the broken faces, you can move edges and vertices if needed to return the edges to planarity.
[image: Click on the picture]
It might be in some cases better to rotate some of the edges about the hidden edge is the right thing. You could also trim to intersecting faces as in your second screen shot.
In your last one, you can't make that shape without the triangles because the edges aren't in the same plane. This shape is similar to a boat hull. If you look at plywood hulls, they are developed from multiple planks. There is some bending and twisting that each plank can tolerate and when it's all assembled, the hull is very strong but there is a limit to how much bending you can put in. Thus the need for multiple planks.
Again, in SketchUp all edges must be in the same plane to get a face between them. It shouldn't create any problems for you, though. You could use a different program that uses NURBS for modeling. You'll not be working with flat faces as in SketchUp but it won't give you a good representation of your plywood-skinned structures.
