Set the eyeLook strengths low in the Strength panel, or remove those 8 keys.

The lips are joined in the mesh. Press Cut Lips, then generate again.

No. The face landmark models ship inside the add-on and run in Blender.

Yes. They are normal Blender shape keys. Sculpt on them, scale them with the Strength panel, or generate again.

Partly. Use Guided mode if the automatic search finds no face. Mouth and brow shapes work. Blinks and eye shapes do not work well on flat anime eyes, so keep the model's own blink shapes.

No. FaceKeys builds a helper rig in memory, makes the shape keys and throws the rig away. Your scene only gets the shape keys.