Hey Jouska! Turning off the Freeplay Zero shouldn't be too difficult (from a software perspective). In the main menu, you can hit the START button, and somewhere in there is a shutdown option.
Offhand, if I recall correctly, the shutdown script is located at /home/pi/Freeplay/Freeplay-Support/shutdown_daemon.py
It should look like this:
https://github.com/TheFlav/Freeplay-Supp..._daemon.py
Here's the line that tells it which button (GPIO) is used for shutdown.
STOP_REQ = 20 # Stop/start button input, active low to shutdown RPi
As for the hotkey feature, you can change the hotkey. A lot of people use SELECT as a hotkey.
From the main menu, hit START. Then select CONFIGURE INPUT. Hold down the A button to start the process. For any button that you don't have, just hold down A to skip it. When you get to the last item, it's HOTKEY. Just tap SELECT (or whatever else you want the hotkey to be). [I would normally double-tap the power button to define the hotkey as power.]
Now, having said all that, if you need a new power button, you should let me know. Maybe the real solution is to just replace/repair it. Go to
https://www.freeplaytech.com/contact/ and select the SUPPORT option if you want help with that.