I don't have much experience with animation but from what I can say you can keyframe their value as any other input Blender have with the key "i", if the shapekey is highlighted in purple that means that it's being controlled by a driver.
I would appreciate a more detailed explanation of the issue.
With the facial rig, there's one bone that slides me mouth hole over the mouth surface. Btw the wide mouth was intended to be controlled with the custom properties of that bone, this can be removed if you want but I think that was your issue.
If you want to add more shapes to the mouth then you must add more shapekeys, I recommend watching tutorials if you don't have experience with them.