I'm renovating the third floor of my house. It's a old semi with brick walls on the outside. We are leaving the shared brick wall exposed but I need to put a 2x2 wall on the exterior wall to hang some the dry wall. Should this wall sit on the floor joists or is it fine for the bottom plate to be attached to the subfloor. I also need to build a half wall around the stairs that come up to the third floor, in a U shape around the opening. Can this wall also sit on the subfloor?

These are non load bbearing walls and can sit on the sub floor. However, I'd recommend 2x4 for the walls and not 2x2. More strength, less warp, thicker insulation, etc...