Not true. Lords need 5P to get appointed. So I assume Dukes need at least that, probably more.
You can run in lordship elections with just 1P, but thats only good in republics and democracies.
No way...I once couldn't appoint a duke because he needed 3P.
I never had the thing where 5P for a rural lord. I think I got one once with 2P or something on Garret in Ohnar.