I am attempting to find out if I can use a Pololu Dual VNH5019 Motor Driver to power my stepper motor.
1.) Can I use this shield for that purpose?
2.) I want to power two stepper motors which should do exactly the same. Can I stack two Motor Driver on top of each other to operate the two stepper motor with the same pins of the arduino?
3.) I would like to power the Motor Driver with stabilized 24 V. Is it possible?
You can find answers to most of your questions in this post by Jeremy. To summarize, yes, you can use the dual VNH5019 motor driver to drive a stepper motor. You can find some example code for doing so in this post. Please note that this code is for the MC33926, but works the VNH5019 if you comment/uncomment the indicated lines of code. You might be able to stack VNH5019 shields, but it would be difficult since you would need to remap some of the pins and modify the library to use different timers for the additional shield. Please note that if you want to control 2 stepper motors, you would need to use an Arduino with at least 4 timers, such as an Arduino Mega.
As far as powering the shield, a steady 24V power supply should be fine; however, please note that while the overvoltage protection on the VNH5019 typically starts at 27V, it is possible for it to trigger at voltages as low as 24V.