Why would you need insulation on the ceiling in a basement? Since the ceiling is touching a heated space itself, there is no need if you will then be using the basement too. Insulation there should be done only for soundproofing, unless you have radiant underfloor heat installed, in which case, the insulation should have been done already as part of the installation. So insulation really only offers soundproofing value. So the question is, how much noise will be generated there?
Counterbalance that with the rationale for leaving this space accessible. I've often enough needed access to the underfloor regions of my home, for wiring changes, plumbing changes, repairs, etc. So any insulation may be better done as fiberglass batts anyway.
As far as the walls go, filling the cracks is a reasonable idea, IF they are stable. If the walls have moved due to frost heaves, etc. and might continue to move, I would ensure they are stabilized before you cover the wall over. A buckling foundation wall is not something good to have under your house.
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
I think based on the comments I better understand your scenario now.
Building Science has a lot of great information on basement insulation and the suggested method is to use XPS foam against the walls, optionally bats between the studs and no vapor barrier (since the XPS foam is the vapor barrier).
I would suggest that you use 1 1/2 - 2" XPS foam against the walls, and then space your studs another inch or so away from the wall (to allow your water to drain). If you need higher R values then the XPS provides you can use bats between the studs and I would suggest something like Roxul insulation which is stone wool instead of fiberglass since it is not affected by moisture like fiberglass is.
It would also be advisable to use steel studs so that they don't rot should they come in contact with moisture. You might also opt to put the bottom plate on top of a piece of XPS foam so that there is a less likelihood of the metal studs rusting.