Any way of knowing what the compass icons mean, other than investigating them? Perhaps a legend of some kind.

farms are farms and not all are settlements you control. Some of your settlements are not farm icons. Some are unique such as the drive inn movie screen, the obelisk tower, and some others. There is a school icon but no schools are still schools. May be 1 hospital icon, metro stations share one and factories. None of that tells you what is actually in any building now.

Yeah, now that you mention it I can see that they are all very generic looking icons. I guess exploration is the way to go. This game sure doesn't give you a lot of info, not that it's a bad thing, it actually makes you have to play it.