1. At that moment you can't have it all: a 2D Plan like in AutoCAD and a good 3D View. At least not yet. The main purpose is "interior designer" not a professional CAD program.
2. Wile this cutout is needed only here and in this position I opt to make it locally:
2.1 When generate the staircase uncheck "Generate cutout"
2.2 At upper level, draw the rooms then modify needed room to make a desire hole (on a room corner) over a part of staircase. In this way you will have also the correct surface of that room.
3. You could try to combine parts of staircase.
Remember: a staircase it is a piece of furniture. If the top of it (including balusters) it is a little higher than the upper level the entire object will be visible also from the upper level.
If you make the correct combination you will see only what you want even in 2D Plan.