You can always spray foam over top edge of the wall layer of XPS, this ensures that there's no air leakage from behind the XPS on the wall going up. I'd also make sure you caulk/tape all seams between XPS boards, and spray the bottoms/corners so it gets a real good seal from air movement.
Well... THAT's an expensive house to heat, what with Lake Effect and all!
I think it'd be fine to slip some styrene (pink) foam board into the gap. You could also use polyisocyanurate, but you wouldn't get the benefit of the foil facing because you wouldn't have any air gap.
If you add foamboard, or even if you DON'T, the vapor barrier should ALWAYS be on the HEATED side of the insulated wall in cold climates. That means on the LIVING SPACE side of those studs. Right now, your vapor barrier is gathering moisture (frost) between it and the fiberglass, and when it melts your fiberglass gets wet. On the CORRECT side, it stops any moisture from getting into the fiberglass in the first place, trapping it within the living space where it belongs.
Upstairs... I'd leave the existing fiberglass in place, but strip off the drywall. I'd span the "studs" with heavy (2" thick) horizontal furring strips, and I'd fill the gaps with 1-3/8" polyisocynanurate foam board (foil faced) snug against the existing "studs". I'd seal all joints with aluminum tape. Then new drywall can be added to the horizontal strapping, leaving a 5/8" air gap between the foil-faced foam and the drywall.
In fact, that's exactly what I DID in this house - it's a transitional-timberframe 5/4 cape in Vermont, and we now burn just over two tons of wood pellets (about $500US total) per year, just about 1/3 as much as we burned the first winter, before we did that foamboard job. It was interesting to get the switches & outlets out to the new surface, but I accomplished it by cutting pieces of plywood with box-shaped openings & stitching them into place across the studs. I screwed the boxes into the plywood carriers (mounting ears reversed), so the boxes are just less than flush with the new drywall.
Funny to run a studfinder on these walls, though - studfinder only finds HORIZONTAL studs. 8)
Best Answer
For covering exposed XPS, especially on foundations (though not limited to there) "Parging" (pretty much a layer of a stucco-like product) is fairly normal; you can get stuff marketed for exactly this job, or not, as you prefer. In the typical thin application, it provides sun/UV protection and appearance similar to concrete, with a minimal level of impact resistance.
In a more abusive location a full stucco coat with reinforcement may be needed.