as far as i know, having a castle in the province simply doubles the resources available from that province; in addition, the administration value of the fort returns that percentage of resources from neighbouring friendly provinces.
the only complication is when having overlapping forts.
dominion has no effect i believe, though it may increase resources by dominion %. Unrest reduces resources by the unrest number as a %
you don't get any gold from unowned provinces, correct.
also, the gold income of a province w/ a fort is increased by admin/2 %