I am not able to duplicate the problems with the baseplate visibility in section or the missing face in the foundation. The foundation shows all 101 entities in Layer0. Changing the roof framing layer visibility does not affect it for me. If we are seeing that no other users are experiencing the same problems with your models as you do, you might try Unchecking "Use fast feedback" under "SketchUp / Preferences / OpenGl" tab. (i.e. that would indicate a graphics card problem). Check if the graphics card driver is up to date.
Clearly you don't want faces and edges to be on other layers besides Layer0. Only assign other layers to groups and components. If you are following this, at it seems you are trying, then the only thing I might suggest is to try the "Default layer geometry" plugin to periodically check that all your edges and faces are in Layer0.
In regard to the section / baseplate question, view the model without the section cut selected, but active. Also uncheck (off) "View / Section Planes". Why don't you set up some scenes using sections that you want, and see how the scenes turn out?