When i first built my home, adopted Runa and got a steward i noticed things would be a little out of place every time i left and came back. Not a big deal. I thought by closing some doors and display cases i could keep the changes to a minimum. When i left the house for a long time and came back i found someone had opened the doors and display cases and all taken the items out.
On the flip side of this, there were many items added to my home and even set up in a nice way. That made me happy.

Is this all common and normal?

I've never seen that in regular houses, but I don't have Hearthfire yet.

Maybe little Runa likes doing a bit of decorating.

yeah, it didnt happen in my regular houses. just the one i buit with the hearthfire add-on.

Some of the items you display seem to move, in particular, the unique items. Harkon's sword, Volendrung, even Zephyr kept moving in its display case a little bit each time I came home until it was eventually sticking through the side.

Is it just specialty items that are moving? And where did you put them? Apparently all the clutter that comes with the house respawns if you are not there for 10 days. So if you take something off a table in order to display one of your trophies, it will respawn if you aren't home for 10 days, causing the item you placed there to fly off somewhere. Display cases that start out open will respawn as open even after you shut them if you aren't there for 10 days.

Sounds like you paid your steward to furnish some rooms, and they aren't finished yet. So everytime you come home, new stuff is added to the rooms, and some things may be moved around as an effect of this. This trick to decorating any home ever since the game's release (because this bug never got fixed) is to drop stuff on the floor, then leave the house. Then come back in and drag the items where you want them. After that, they stay put.

...you know, that trick doesn't work as often as people say it does. >_<

Well, it does work for me.

When you are away for a long period you usually come home and all the doors are closed and the display cases open. The house resets after 10 days and respawns everything that was originally in there. I have never known anything to arrange itself, so you will have to get us some screenshots of this phantom house decorator's work.

Those weapons moving a bit in the display case is normal, and you should always have the display case closed if you have something in it, otherwise yes it might end up elsewhere. It could end up getting out of the display case even with it closed, but that is a glitch, or you never dropped the stuff on the floor and left before arranging them.

Came back the next day and my troll skull was in a bucket and my dwemer thingy was in a bowl of berries.

sorry about that i thought i would steal some stuff to pay for my skooma habit

Holy crap. Thanks for that.