Playing as Altar on 1.06.

When the destroy building button (shovel button), the cursor changes in that pop up window, but when moved out into the city display, it changes back to the normal feather, so you can't destroy any buildings at all. When you move the cursor back over the build display, it remains a feather.

I also had a city get attacked by a monster and the garrison lost, but nothing happen to the city and the monster just stood there. Relief forces showed up and got rid of it.