1. In Blender, it seems that once I do a number of operations on an object, it gets subdivided into surfaces, sometimes in very unexpected ways (for example, it seems that a single surface can't have any holes, so it gets split in a way that there are no holes.--Am I correct in that assessment?)

Yes, every surface is defined using triangles. That's how every program for 3D modeling works. Sometimes there are quads but they usually get converted to triangles.
On my site dodecagon.nl you can find a manual called Vertices, Edges, Faces, and Meshes that does a little more explaining.

But in Blender, that face is subdivided into multiple faces (see screenshot) and I have noticed that if I apply lots of operations, there may be hundreds of subdivisions. Do I have to name every surface in Blender?

No, of course not, that would be almost impossible. What you do is define a set of material names. Then you select a set of faces (the triangles) and assign a material name to that group of faces. You do that until every face is part of a group with a material name. While in Blender that has another advantage: you can select (or unselect) all the faces that have the same material assigned. Very handy if you don't want to smooth everything but only a specific set of faces. (You don't want to smooth glass surfaces.)

...but if I have an object that is 20" or 50-ish cm high, it imports into SH3D as about a quarter inch high,

As I said in my previous response: Import with magnetism OFF. That prevents a conversion rounding from metric to imperial on the imported object (the internal object definition). The display will be in imperial but the actual object will remain metric. There is no program that I know of that can save an object in imperial measurements, no matter what file format you use, it will always be stored in metric.
You can create a model in Sweet Home 3D or Blender using imperial. When it is saved the values in the saved file will be converted to metric. When you import in Sweet Home 3D switch magnetism OFF, that insures that the actual metric values in the file are imported and not converted back to imperial. Only the display will be imperial. If there are still differences than that is because of different rounding between Blender and Sweet Home 3D. And that is very likely because the smallest value in Sweet Home 3D is 1mm, it's interior design software, not 3D modelling software. On the other hand Blender is 3D modelling software and handles values much, much smaller than 1mm.

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The 1mm limit of Sweet Home 3D is not completely true, it does use smaller values internally like when you import an object, But every value displayed only has one decimal making the smallest displayed value 1mm. I'm not sure how that translates to imperial. You can enter a (metric) value like 0.05 but the display will round it to 0.1, internally it will keep the 0.05.
To get around this I often create models on a scale of 10:1 or 100:1. Only the last export of a model is down sized to the required size and sometimes I even don't do that, a model is easily scaled down after you import a large sized object.