Here is a video of the homing procedure. X and Y are homed sensorless and Z with an regular endstop.

With the help of Uzair Patel I was able to solve the non-linear Z-Axis firmware problem. I decided to use marlin 1 instead of marlin 2, because marlin 2 takes way longer to compile in the arduino IDE than marlin 1.   
I added the extruder and the  Bowden tube to the printer.

And here is a picture of the "folded" Bowden tube.