Is it possible to lift heads you chop off? And lay them on a shelf for example? Just curious. Never been anything but a Mage so..

Tried it with Roggvir (the guy who gets executed near the main gate when you first enter Solitude), but was not effective. It's very hard to lift the head up, and when it's dropped, it just rolls off and clips through 90% of things.

Yes it is possible and you can throw it about and I never seen it clip.
The havok engine(?) does not spaz out any more with a head than it does with a part of a skeleton...

Yes! You can totally lift any head, but it stays oddly connected to the body (much like sometimes weapons do until you put them in your inventory). They also seem to be abnormally heavy, almost as if the entire weight of the body is being used for the weight of the head when you try to lift it. When I lift them, general rule is to do it very slowly, especially when lifting vertically. Moving horizontally is a little better, be sure to be walking only.