Hi @yasemin0, welcome to the forum 
Note that the Pixhawk 2.4.8 may not run as well as our recommended autopilot boards.
QGC is ground control software, and is not intended to run on the vehicle. I’d recommend following our software setup guide to configure your topside computer so that it can connect to the Raspberry Pi, which then acts as a communication bridge to the autopilot.
Wireless use of a PS4 controller is currently not actively supported, but I’m unsure what the limitations are (if QGC is able to detect it then it may have an unexpected button configuration, or could be missing some button functions or something, but might still be generally usable).
Assuming it’s able to detect your controller, QGC should handle sending the relevant commands to the vehicle, depending on how you’ve configured the joystick functions