I have the problem that my laptop does not want to remove itself from flight mode. I'm then told, "Use hardware switch to turn off", but unfortunately I have absolutely no idea what to do now
You were told to turn off your laptop with the hardware switch. Then restart it… If it works, everything is fine.
It sounds like you've activated airplane mode using the keyboard.
See if you have a button with an airplane on it. Maybe a lamp shines on it. You may have to press it together with the Fn key to turn off airplane mode (Fn + airplane).