Hm, well, I believe the reason I found it hard to answer the first question was because I couldn't think of any
disc-shaped objects that didn't already have a name. For instance, the once you mentioned are called
diskus and
puck. Considering we are not as keen as the Icelanders to create new words with domestic material, I believe we mainly have loan words or compounds (such in the cases of
brödskiva, glasskiva, etc) for such
objects. (Then again, if you have more examples I'll gladly translate them, I just can't find any myself.) So, it was not just the word
any, although it might have confused me since it gave me a feeling of that there were many such objects (yet I couldn't think of any).
Also, it might be too early, but so far, it seems to me that a
platta is more solid than a
skiva. For instance, a building could be erected on a
betongplatta (
betong - concrete (building material)). Here, the focus is obviously on the
flatness, focusing on the flat surface of the concrete, rather than the
sliceness (since there can be no such thing as a smaller
slice of concrete originating from a bigger whole, unlike in the cases of bread, wood or cheese).
Additionally, and this might count to your first category above,
platta has an additional meaning, namely (cooking)
plate. Then again, the full name is
spisplatta (with
spis of course meaning
cooker), but when I use the word
platta alone, I normally associate it with a
cooking plate. Again, the focus is on being flat rather than "flat and part of something bigger".
Interestingly enough, a really big flat stone, used as a foundation could be both a
platta or a
skiva, but in order for it to be a
skiva, it must be very thin, I sense. Yes, something that is used as a foundation is almost always a
platta. Maybe it matters whether the thin object is vertical or horizontal (obviously the
flatness is more prominent with horizontal objects).
I'll do some more thinking, that was all for now.