If I played the robber baron castle in my opponents city, can I use the pawnbroker to get its resources back?
Yes, you can.
German FAQ: http://www.siedeln.de/faq/315_632_de.html
And second, since it is in my opponent's city, can my opponent use the pawnbroker as a way to get rid of the robber baron castle, as it is a building in his city?
No, you can't use the pawnbroker on enemy buildings.
German FAQ: http://www.siedeln.de/faq/138_807_de.html