In theory you are right, however sometimes the A300 shows it age and it just ignores it and plays the sound regardless.
Virtually all operators have the "DH -5" in their SOP to stop the sound from playing.
As for the first issue, you can try this:
We will add deadzones around the set points in the next version, that should remove those issues.
Which tiller axis? From my knowledge, there is only a "Nose Wheel Steering Axis", but that works as expected for me