Are there any (more or less) simple test devices for capacitive touch screens, e.g. something which I can attach to a touch screen and which is able to do capacitive inputs at fixed locations (ideally, it contains a matrix of such locations)?
I don't know enough to be sure but I suspect that any matrix you put across the screen will cause stray capacitance problems and make it very difficult to know what exactly you have tested. A much more definitive test could be done with one of those flexible rubber topped capacitive touch-screen stylus pens and a robot or 3-axis pen holder. It should be reasonably straight forward to modify a cheap 3D printer to a 3-axis CNC. Replace the extruder with a pen holder, figure out a few G-codes and you can automate your tests quite realistically.
Tappy might give you some good ideas.
I expect that with this method you could easily check sensitivity by monitoring the Z-axis value that is registered as a touch on the display. All sorts of possibilities are then opened up such as giving a "heat map" of the sensitivity of the various test points, etc.