The Pope is fallible. It is only in very limited instances when the Pope is infallible-the only instances of such Infallibility to date is with regard to Mary's Assumption.
The Pope is the Head of the Church as chosen by the College of Cardinals. Because we are all fallen, even the Cardinals can get it wrong. Thus, even if a Pope is way wrong, that doesn't ipso facto negate his election. So he IS the Pope just like Obama was President.
As for resignation, that is what Benedict XVII did so yes, it can happen.
I hope that helps.
Just ignore this Pope.