Great news – great sailing to come!
Before commenting on your original query I will strongly second Mike’s suggestion to add secondary means of holding the rudder up. Ideally two lines, one to each quarter, which helps hold the rudder amidships. See photo of Helene’s arrangement when I had her:
Rudder safety line to keep it in the raised position
On your first point, definitely protect the mooring lines, rudder and rudder lines from chafing each other.
One thought to keep the rudder away from the mooring lines is not to raise it completely – leave it just submerged so that it does to foul the moring lines. The issue then changes to how to prevent damage when taking the ground.
Leaving the downhaul slack would allow the rudder to rise on grounding and drop on floating. However slack uphaul / downhaul lines can lead to them slipping off the blocks through the transom or in the rudder and jamming.
You could rig shockcord to keep the uphaul / downhaul tensioned at all times. Lengths of shockcord passed vertically over the horizontal uphaul/downhaul lines in the aft cabin pulling towards the cabin floor would keep them tensioned? (Helene had more complex shockcord arrangements to keep the lines tensioned).
An interesting challenge! Let us know how you get on.