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I recently put my first rig to a model with rigify, the problem is that when I go to pose mode some parts of the model do not move as you can see:
You need to add weight painting to this part of the mesh as well. First click on the mesh (model) then keep holding the shift button and click on the rig then hit ctrl+P then select parent with Automatic weighting, this should fix this.
parent with Automatic weighting
Don't know if I will be much help but, have you parented the Facial Objects to the Main Head. Parenting them should allow them to follow the Head when you move it.
Hope this helps.