The little icon in the top right corner changes to a triple arrow when that unit (or some of them) are in motion. It's the little diamond otherwise. Stationary structures get the little diamond all the time.
I think the backdrops are supposed to be orange for military (anything with a gun) and green for everything else.
However harvester exo-forcefields and the new human cities show up orange, and they aren't armed so I'm not 100% sure.
D.