just like for NPA, the AP will trip -50 feet below min to be sure that you are not going to continue....)
Depends on the plane i guess?
AFAIK it is not a requirement and on "my" type the AP doesn't trip, you have to actively switch it off. Sadly no EVS yet although boeing announced it 7 years ago, seems there is no market for CAT IIIb plus EVS.