yea, it's because the system cant find a valid contiguous spot to place improvements in that city... In the first example if you actually complete the iron mine I would bet it will then let you build improvements (spawning them on the other side of the mine). I personally would like for the spacing of dropping improvements around your city to not be something you need to worry about but it may be something out of our control for release. I'll see what can be done.

You can build on swamps.  I think the problem that Nefaste is referring to is that the cities are so close together that they cannot build towards one another, and are prevented from building away from one another by the rivers/other terrain features.

One thing that you might be able to do in this situation is demolish the pier/dock/harbor/watermill and rebuild it on the other side of the river - I was able to order the city to build on the other side of the river after the pier finished building the second time.  You might have to order the pier rebuilt the same turn you demolish it.

You can't build on Swamps, or at least you used to not be able to. But you can use "Raise Earth" once on each swamp tile, and then build on them afterwards.

Also note that earth magic really comes in handy here, as you can raise and lower terrain, and once level, gives you addition space to expand your city.

I've done this many times on the edge of the ocean. Dont' know about up against mountains.