Is the obvious movement in the anus that one feels during ablution, prayer, and rising from prostration considered a discharged wind?

The ablution of one who has invalidated it is not accepted unless he performs ablution again. Invalidation (hadath) here refers to the emission of wind, and one must be certain of its emission, not merely doubt or suffer from obsessive whispers. So, if a person is certain that wind has been emitted, their ablution is invalidated. However, if they doubt and do not know whether anything was emitted or not, the default is that their ritual purity is valid. It was reported to the Prophet (peace and blessings be upon him) that a man imagines he finds something (i.e., passes wind) during prayer. He said: "He should not leave until he hears a sound or perceives an odor."

Therefore, ablution is not invalidated except by absolute certainty of its invalidation. Mere feeling of movement does not invalidate ablution until you are certain of the emission of wind as is commonly known.