It is, but you have to give it a status effect first. Sleep and freeze is the most helpful (though you have to get lucky to get a freeze). Without a status effect, Mewtwo was coded to be caught in nothing less than an Ultra Ball.
The best thing for a wicket keeper (or any close infielder) is that you must, on every ball, always anticipate that the ball will come through to you. Keep your...
Yes, but it's a wee bit harder than waiting. Quick balls or fast balls (from yellow Apricorns, give them to Kurt and wait a day) should be the best way...
It disappears from the game. Knocking out Zapdos, Articuno, Moltres, or Mewtwo removes them from the game completely. That's why you should save your game before trying to catch it,...
It honestly depends. You could consider the Pokemon your first encounter, and catch another after the mandatory knockout or ignore it and catch something else when you can get some...