Earlier, you wrote, "are you suggesting, then, that Jesus appointed someone who did not believe Christ's teachings to carry on these very same teachings?"
I responded, "He didn't appoint Judas Iscariot to carry on His teachings. He appointed Judas to betray Him."
Do you agree? Or, do you still hold to your claim that Judas must have been a true believer in order to be appointed to the twelve? Maybe he tagged along because he thought it could be advantageous to align himself with this guy who might be the promised Messiah who'd overthrow the occupying Romans. At any rate, Jesus knew his heart.
Oh, and be sure to check Romans 9 for the answer to that "God destined someone for Hell?" question you posed. At the very least, no matter what we might think of the idea, it's apparently not unthinkable.