You're absolutely right - forgive my mischief! The solution is of course to choose the opposite door to whichever guard replies to the question "What would your colleague say if I asked which was the door to freedom?"
Well, in your first solution (1) this is only of practical use if you know he is the honest guard - which, according to the scenario, you do not. As for your second solution (2), you have simply strayed into the realms of sophistry by suggesting that the guard must double guess the prisoner...
But these answers assume that the asker is aware of which guard lies and which one doesn't, but this is not stated in the scenario given. Only by asking both guards a question can this be found - but again, the original scenario does not allow this.
''Prisoner is put in a room with 2 doors. 1 door leads to freedom, the other to excecution.
Next to the doors are 2 guards. One of the guards always lies, the other always tells the truth. The prisoner is allowed to ask one of the guards one question to figure out what door leads where. What...