It actually is a paradox, just not a cool one.
It isn't, because there is only something preventing both from happening. It would be a paradox if both were also forced to happen.
# Your mission is not to accept the mission. Do you accept?
No. The mission is now complete. I no longer need to accept it.
# If the temperature this morning is 0 degrees and the Weather Channel says, "it will be twice as cold tomorrow", what will the temperature be?
Unless that's in degrees Kelvin, just cut that temperature in half. If it is, the weatherman is a liar.
# Answer truthfully (yes or no) to the following question: Will the next word you say be 'no'?
Umm... No.