Hi Noktok, Welcome to the forum!
ArchiCAD doesn't have a 'hide wall' option, but a really simple method of showing only certain areas in the 3d window is to draw a marquee on plan then go to 'View'>'Elements in 3d view'>'Show selection/marquee in 3d' (or press F5). Only the objects within the marquee will be visible.
Regarding your door problem, in the settings dialog there is the option to set the Anchor of the door relative to a particular storey. This is what the cill/header value relates to.
An option I find very useful is to turn on the ghost bounding box, which gives you the outline of what ever you are about to place in both the floorplan and in the 3d window. You can tell immediately if your door is going to positioned on the incorrect storey before it is placed.
This is stored in your work environment settings, so go to 'Options>'Work Environment'>'On screen options' and tick the Bounding box option.
Hope that helps.