Any opinions on whether the door to the run should open inward or outward?
People do it both ways. Chickens are not likely to knock you down and trample you, especially if you are 6'-1".
If it opens inward it needs to be high enough so the bedding doesn't block it. If you lived somewhere that deep snow id a problem you might want it to swing inward for that reason.
If it swings inward that takes up some wall space to put nests, roosts or other things. That's a reason to swing out.
Most building materials standard dimensions (cheap sizes) are 4' or 8'. If you use those in your design you can often reduce cutting and waste. You have to be careful on using center-to-center or out-to-out measurements so you don't mess that up but if your high wall is 8' you may reduce cutting and waste. Just a thought.