The main issue is that you forgot to apply the rotation to the mesh. This causes this weird behavior with the model tilts her head. You have also the Armature modifier multiple times added to all objects, especially the body which has it 9 times!
I'm not sure if it's intended that you use the metarig as an armature. You can do this for the quick pose but it's very simple and has no controls, IK, or tweaks. The Rigify rig is the generated rig. You need to press the Generate Rig button to create it.
Steps to fix the model:
- clean up the modifier stack of all mesh objects and remove all Armature modifier
- apply Ctrl+A, All Transformations to all mesh objects, this includes Rotation, Scale and Location. (The metarig needs to have this applied, too. But you have already done this.)
- parent to all mesh objects to the rig with Ctrl+P, With Automatic Weights
- use a Data Transfer modifier to transfer the vertex groups from the body to the other objects (eyes, hair, tear line, teeth, tongue, etc) if needed. Done this in the example for the eyelashes.
- make sure the Armature modifier is on top of the stack but behind the Mirror modifier if present. Subdivision Surface modifier is last (on bottom).
Hair parented to an Empty which has an Armature Contraint (head bone) as suggested by James in the comments and tilt the head a bit more: