I just got a GX7, and I have the 12-40mm on backorder. In the meantime I'm using the Olympus 17mm and I'm quite pleased. The autofocus is very good, and the lens produces nice sharp images. I'll report back on the zoom once I receive it.
As for shakiness, yes that's always an issue, but I'm hoping the GX7 in-camera stabilization will be enabled for video in a future firmware update. In the meantime I'm just relying on old fashioned technique, just like the old days. Adding weight to the camera is another thing I might do, just do dampen those lightweight camera jitters and bumps.
It's good to know there are decent stabilized lens options out there, too, if necessary.