Armor Stands

Can confirm. I guess this relates to the fact that fence is a 1.5 high block and placing it directly to the fence places it inside of the fences hitbox. When dropping the armor stand
from above it behaves as you would expect: floating 0.5 blocks above the fence.
It's a bug , but I don't think this is worth fixing, because you'd have to add an exception to the code just for the fences and fence gates. ^{but don't ask me, I'm not a game developer}

Also for the door thing: It's possible to get an armor stand onto a door, but you have to use some pistons to achieve that.