1 on the interior wall between the heated and unheated portion of the basement i would not use with a vapor barrier.
Vapor barrier framing a basement wall against concrete.
That is if the studs are going to touch the concrete wall.
If you have a framed wall that is adjacent to a concrete foundation wall where the vapor barrier is next to the drywall in front of the studs the fiberglass insulation gets wet and becomes a breeding ground for mold.
Also be sure to use treated lumber for the bottom plate on the wall framing.
The construction of the wall for instance is vital to the use of a vapor barrier.
Before framing the walls of your basement install a moisture barrier to prevent water and moisture from entering the wall cavity.
In winter the dew point of the interior air is typically about 50 f assuming an air temperature of 70 f and a relative humidity of 50.
When the mold grows it will spread to.
The other option is to set the 2 4 wall framing in 4 from the masonry or concrete basement walls and use just the vapor barrier on the insulation facing toward the living space.
Here are three different types explained.
Most jurisdictions require a 4 mil plastic sheet vapor barrier for basement walls against concrete.
I would think that trapping any of this moisture behind a finished basement wall would be bad.
Or you can leave a 4 inch gap between the studs and concrete wall and probably get away with it.