How stable is this thing?
Surprisingly it is quite stable. If you are going to use it on a desk (and keep it mostly in one place) you could use some double stick tape under it to keep it positioned on the desk, especially if you plan to type or do something other than watch videos.
The thickness of the iPad fits nicely in the space without feeling like it is going to slip out, plus it is wide enough that it is not going to tip side to side. I don't know about with the Apple case, probably too thick.
If you are worried, guess you could use some scotch double sided tape (the thin style) inside...?