Are "stucco" finishes for foam board insulation available in the US? They're all the rage here, but I strongly suspect if you can live without the texture you can use thinset too and paint it using mineral paint. Don't forget to embed some kind of mesh in the whole thing though, or the seams of the foam board will crack. You don't need any support structure for the foam board if you go that route, just stick it to the wall using small dabs of thinset.
If you want, you can even create some plain-ish "trim" by putting up thinner pieces of foam board on top of the first layer, e.g. around the doors and between floors. Around here you can get all kinds of ready-made foam trim, but I doubt that's available in the US.
I'm not really sure I understand what you want to do about the entrance. Do you want to remove the exterior wooden stairs and use an existing door into the garage level as the new main entrance? If so, which one? The slightly better-looking door half hidden behind the tree or the rotten something underneath the upper-level balcony?
In either case I'd only do that if the opening is tall enough for a regular door. If that works out ok, I'd install a decent-looking door, flank it with lights or flower pots, maybe trim it a little and voila, you've got an entrance. Then you can remove the wooden stairs, fill in the railing and have a balcony.
Otherwise I'd strongly consider enclosing the stairs and balcony.

