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From my reading of the rules (others may want to jump in and correct me):
What happens if one of the Wagons is captured?
1. Presumably the Catholic player only gets VPs for 'owning' a Wagon at the end of the scenario.
Correct, per 15.0 of the series rules.
2. Presumably the Catholic player cannot move the Wagon as he has no means of allocating it to a Wing.
Also correct, per series rule 10.89 (captured wagons are treated the same as captured artillery).
3. What if the Protestant player recaptures the Wagon? Can he move it again? It is possible that by this point the Trosswaibel has been removed from the game as per 5.3.3
Guns and wagons, once captured, can never be recrewed, so cannot move even if recaptured.