For the bridge across your moat:

I found this interesting video on YouTube covering the building of a stone bridge in 13 days for $13,000 and with a crew of 5.  Now, I must confess that this bridge isn't a "true" stone bridge made with fitted pieces, abutments and keystones and all that, but one can see that adapting an honest facade to the method used in this video could net a fully functional bridge that looked like a proper finely crafted stone bridge rather than the rubble-style used here. Perhaps a similar technique could be used for the walls of your castle?  Who knows, there may be many possibilities!