1. Are you sure they were "suppressed" in SW and not just "hidden"? There is a known limitation that if you import SW model with hidden components using "Appearance" Part Grouping mode, then the hidden components will still be displayed. If you import using Automatic part grouping mode, then those components should be hidden (Opactiy set to 0%). Suppressed components should never import so I'm guessing they were hidden in SW, which could result in this behavior. Again, try importing using Automatic grouping. (Unfortunately, all your like appearances won't be grouped as a single part, so you'll have a bit more work to assign like appearances... COPY and "Assign Appearance: [copied appearance" will be your friend.)
2. If I understand this correctly, then it is intended. This won't happen if you import with Automatic mode as described above. When you import with Appearance grouping, then every SW part/component/face/etc that has a certain appearance, is grouped under a Visualize "part" which contains ALL GEOMETRY with that same appearance.
Thanks very much for the assist! As it turned out, some parts were suppressed and others were hidden. Once I imported using Automatic mode, everything was as it should be. I watched a few tutorials, but obviously missed any mention of this drop-down.