It sounds like you're saying your basement is heated, but nothing else is (possibly the floor above is exposed to the outside).

What you've done is put in insulation below the subfloor to try and keep the heat in the basement. This is a good idea, however, any time you have warm meeting cold, you're going to get condensation, and so you need a vapour barrier on the warm side only. This prevents the moisture in the warm air from getting into the cold zone.

If you have the vapour barrier on the cold side, you'll get condensation on the vapour barrier itself, between the insulation and vapour barrier, and this will lead to mold (and it's possibly a worse thing to do than have no vapour barrier).

If you have vapour barrier on both sides, you'll also run into trouble as if any moisture DOES make its way in between, there is no drying and no way for it to get out.

If you're using batt insulation, the best thing to do is put a 6mil vapour barrier on the bottom side of the joists, and seal it as best you can around the edges. Ideally you want a continuous barrier with no gaps. The vapour barrier on the ceiling should be connected to the vapour barriers on the walls, and then is typically sealed to the floor using acoustic sealant.

Foam insulation works as a vapour barrier as well, but you need to ensure all gaps between each piece and around the edges are sealed using air-tight tape (eg, Tuck tape).

Realize though that having this vapour barrier in place once you're finished construction will actually be detremental. You don't want to vapour seal between heated rooms, as it inhibits natural drying and air/moisture movement. If you end up having the basement unheated (or minimally heated), then it becomes the cold zone compared to your first floor and so your vapour barrier will be installed on the wrong side.

Ice forms in that location because 1) heat is lost where the two panes of glass are connected by the metal frame, and 2) cold air sinks to the bottom of the window opening. I don't see any red flags that indicate air leakage or other serious issues. The fact that the entire glass pane frosts up at times reinforces that position. You have simple heat conduction happening, with little or no air movement from exterior to interior.

I've lived in Minnesota for 25 years, and what you see there is nearly unavoidable in extremely cold weather. It's a result of heat loss through the window and excess moisture inside, and it's the reason window film was invented. I realize that the idea of applying film annually isn't terribly appealing, but it's probably your best bet here, short of replacing the windows. Only low-e glass panels and ultra-modern sealing and insulation, coupled with very good indoor humidity management, will completely prevent ice formation.