Is there a simple way to get Blender to export the model with multiple texturizable surfaces for SH3D?

In Blender you will have to assign material names to all the parts of your model that you want to have a different texture. No need to assign a texture, just any color will do. Assigning a material name will result in a obj/mtl export that has all your material names which you can then assign with a color or texture in Sweet Home 3D. In Blender you can also set how a texture is aligned for each separate part.

2. I can't get the dimensions to export properly in the .obj file. I usually have the scene in Blender set to use Imperial dimensions and Inches, but when I export, a model that has, say a 70 inch side imports to SH3D as 0.2 inches or something else real tiny. It's not a fatal issue, as I can resize it in the import dialog, but it's annoying nonetheless, and seems to be an indication that I'm not really understanding how to properly export from Blender.

Every graphics program is build using the metric system, including Blender and Sweet Home 3D. When you use Imperial then that is just an on-the-fly conversion from metric. The other way around is the same, again a conversion. That will result in small differences that you can not avoid. You can open an .obj file with a plain text editor and all the values you will see are metric.
The easiest way is to always use metric but that might be difficult when you grew up using imperial.

One thing that helps is to switch magnetism OFF when you import a model. After import you can switch it back on (magnet button in the toolbar).
See this post where the same problem was first discovered and the original developer of Sweet Home 3D found the cause of the problem.