Mine (forearm flap) does move. It is anchored only at the back, and I have trained it to work with the "old" tongue. The flap is heavier than the tongue, so it has a tendency to "lean" to the left. I still work on tongue physio to try and correct that (I can feel a pull in the left jaw when I do it).

I have also seen people write of having the anchor released partially if there problems with mobility.

Saliva is definitely down. Immediately after surgery I drooled like Cujo, then the dry mouth hit, and has stuck around, although now (a year later) it is better than it was.