Does the emission of wind, when it is unknown whether it exited from the front or back passage, nullify Wudu'? And does completing the prayer in this state necessitate its re-performance?

Your prayer is valid, even if you are experiencing flatulence, according to the majority of scholars. Doubt about passing gas does not invalidate ablution or prayer, because the default assumption is that no impurity has exited until certainty of it is attained. Similarly, the gurgling sound of the stomach does not nullify ablution unless one is certain that an impurity has exited. What you did, repeating the prayer multiple times, is not necessary. In the future, you must be wary of obsessive thoughts by ignoring them.