Who doesn't enjoy a good storm?

You can change the default wall to be whatever you want. The :DD2WALL: button just starts the drawing tool named Wall, Default. You can edit this to change the properties (advisable to make a copy of it first to preserve the original, but if you want to edit the tool that is used by the button, you of course have to edit the original, and just keep a copy under a different name as a backup). To make it cutable, all that is required is that it is on the WALLS layer. From your images, you are using SS4, and I don't seem to have a problem with doors cutting that wall though.

To make them into single walls, you need to do some manual work. Erase the entire wall (one of them) where there is a complete overlap, and use tools like :CC2BREAK: to split and cut parts out of walls where you have a partial overlap and don't want to delete the whole length of the wall.

In addition to what Sue is writing above, check for double walls. When I look at the screenshots you post, the door is clearly cutting something, otherwise there wouldn't be a white rectangle there. And the wall fill pattern in the second image is offset from the first one, indicating that there seem to be two walls on top of each other there. (The wall cutting functionality only cuts one entity)

I assume you are talking about the Annual Jon Roberts cities here?

I think it is just a color issue, the symbols in this style is quite simple, and mostly white, and the white symbols on the white background makes them invisible.

Note that you don't have to place them from the new map wizard, you can also access these symbols after starting the map by hitting the :ICON_DRAWING: button. (They'll be just as hard to see in the symbol catalog window though, unless you change the view window color from the View menu to something not white.)

1. When you hit the add-on buttons the program loads some defaults to ensure that things work sensibly. For example, if the overland filters were kept when you went to the DD3 add-on, all catalog buttons would just return empty results because the overland filters doesn't make sense in a dungeon setting. Unfortunately, this also means that the settings loaded with the map is lost. Generally, it is not adviceable to use these buttons in the middle of a map. If you wish to load symbols from a different add-on, use :ICON_CATALOG: instead, this allows you to load any catalog, not just the one provided by the defaults for whatever add-on you switch to. The easiest way to reload the correct settings is to just reload the current map, you don't need to restart the program. Simply save the map (if you have changes you wish to keep), then simply pick the map from the top of the recent file list in the File menu. This will reload the map, and reload the settings from it.
2. One way of making torn edges is to place a white polygon with some fractalized edges on top of everything. The white will cover up part of the map, appearing as a tear. Add some inside glow and perhaps some blur or similar to make it look more like a tear and not just a flat poly.