no it doesn't, it is only guaranteed to generate a fun paradox if the prediction was "all predictions will be false".
Earlier there were only about 5 comments, two of which involved this "most predictions here will be false" - however one was sadly deleted and nobody else decided to play ball :D
The paradox would be “this prediction will be wrong”
“All predictions are false” could be wrong, because other predictions are right even though some are wrong.
yes you're right, although I think my example is more likely to exist than the previous.