My recommendation is to avoid applying materials until you know the geometry is correct. Textures tend to make the graphics card work harder so leaving textures out until you are nearly finished with the model will help to keep you moving forward. It’s important to make sure you have only front faces exposed in your model. Especially if you are going to be doing rendering.
After you have assigned materials you can switch back to Monochrome face style to get them out of your way.
Explode what? You should be applying textures to faces in the model. That means you open groups and components for editing before applying those materials.
This is a fundamental thing in Sketchup. If you were my student I would tell you to put this model away for awhile and learn the basics of working with groups, components, and tags with much simpler models. I would also advise you to learn how to look at and clean up components you get from the 3D Warehouse to make them useful before you add them to your file. For example this bed needs attention. Incorrectly oriented faces, way more geometry that is beneficial considering the overall size of the model…
Also make sure that you are purging unused components and materials from your file. It looks like you tried out a whole lot of furniture from the 3D Warehouse and deleted it from the model space. The thing to remember is that deleting a bed from the bedroom doesn’t remove it from the file. It’s like you’ve taken it out and stuffed it into the garage along with all the other furniture you didn’t want to keep. Purging the unused components empties the garage.