Nikon Nikkor 18-55mm VR lens: can you damage lens by turning focus ring on AUTO mode?

I'm a complete novice in photography and recently bought Nikon D3000 kit with 18-55mm VR Nikkor lens. I have bought UV filter as well and while attaching to lens I have turned focus ring when it was on AUTO mode. The focus rim moves when on auto, it jumps like from position to position (has steps and it's not smooth like on Manual mode).It's hard to describe it but I was wondering if you can damage the lens by doing that? I have also noticed that once you shoot the picture immediately after the lens clicks (again - hard to describe the exact sound) like it's positioning itself right after the picture or something. Is it normal for the Nikkor VR lenses?

Yes you can damage the autofocus by turning the focus ring when the lens is set to autofocus. If it still focuses properly, then you didn't damage it.

The abrupt movements are normal.

That clicking probably is the VR, this is normal too. Try switching off the VR on the lens and see if the clicking persists. It should be gone then.

Yes you can damage the AF motor if you turn the focus ring of the lens in AF mode (even if the camera is off with Nikon as the motor is engaged). If the lens does not behave as before and can't get focus right then you do have to worry. As it is, your lens still gets it right. If this only happens in low light then that's perfectly normal.