Does Shepherds/Ambassadors give me gold when I build by moving a settlement?
I would say no. Moving a settlement is not building it.

The rules say:


  The active player must check whether the conditions on red cards have been met after building each single new settlement. If these conditions have been fulfilled, the player immediately records the gold earned on the score track.


This interpretation is confirmed by the BoardGameGeek’s FAQs Shepherds only gives points for built, not moved, settlements and Ambassadors only give points for built, not moved, settlements. Both reference the thread Questions on rules, in which Kingdom Builder’s game designer Donald X. answered:


  No. Shepherds and Ambassadors do not score for moved pieces.