CAR says all followers (small, big, mayor and wagon) can be moved to CC
I just checked
this post. The wagon may be placed to the CC. Good call. Once it's deployed from the CC, it scores as a wagon normally so it may be moved as per the normal wagon rules.
The abbey walls end the road and doesn't connect it so the wagon cannot move from the road into the abbey. A wagon placed in an abbey also cannot move out of the abbey because of the walls.
OK, I'm wrong there. According to the
same post - 7th Question - you may move it from a completed road into an incomplete abbey that's connected to the road or from a completed abbey to an incomplete road that's connected to the abbey. I'll strike out my original answer in the post above.